메뉴 건너뛰기




Volumn 223, Issue 4, 2010, Pages 1372-1467

Spectral theory for perturbed Krein Laplacians in nonsmooth domains

Author keywords

Buckling problem; Eigenvalues; Krein Laplacian; Lipschitz domains; Spectral analysis; Weyl asymptotics

Indexed keywords


EID: 73749086477     PISSN: 00018708     EISSN: 10902082     Source Type: Journal    
DOI: 10.1016/j.aim.2009.10.006     Document Type: Article
Times cited : (50)

References (184)
  • 3
    • 0003237178 scopus 로고    scopus 로고
    • Function Spaces and Potential Theory
    • Springer, Berlin
    • Adams D.R., and Hedberg L.I. Function Spaces and Potential Theory. Grundlehren Math. Wiss. vol. 314 (1996), Springer, Berlin
    • (1996) Grundlehren Math. Wiss. , vol.314
    • Adams, D.R.1    Hedberg, L.I.2
  • 4
    • 73749085023 scopus 로고    scopus 로고
    • Non-negative perturbations of non-negative self-adjoint operators
    • Adamyan V. Non-negative perturbations of non-negative self-adjoint operators. Methods Funct. Anal. Topology 13 2 (2007) 103-109
    • (2007) Methods Funct. Anal. Topology , vol.13 , Issue.2 , pp. 103-109
    • Adamyan, V.1
  • 6
    • 0002095851 scopus 로고    scopus 로고
    • Elliptic boundary problems
    • Partial Differential Equations, IX. Agranovich M.S., Egorov Yu.V., and Shubin M.A. (Eds), Springer, Berlin
    • Agranovich M.S. Elliptic boundary problems. In: Agranovich M.S., Egorov Yu.V., and Shubin M.A. (Eds). Partial Differential Equations, IX. Encyclopaedia Math. Sci. vol. 79 (1997), Springer, Berlin 1-144
    • (1997) Encyclopaedia Math. Sci. , vol.79 , pp. 1-144
    • Agranovich, M.S.1
  • 7
    • 0036771185 scopus 로고    scopus 로고
    • Spectral problems for second-order strongly elliptic systems in smooth and non-smooth domains
    • Agranovich M.S. Spectral problems for second-order strongly elliptic systems in smooth and non-smooth domains. Russian Math. Surveys 57 5 (2003) 847-920
    • (2003) Russian Math. Surveys , vol.57 , Issue.5 , pp. 847-920
    • Agranovich, M.S.1
  • 8
    • 51649138920 scopus 로고
    • Upper and lower bounds of eigenvalues of the classical buckling problem
    • Aimi A., and Diligenti M. Upper and lower bounds of eigenvalues of the classical buckling problem. Calcolo 29 3-4 (1992) 313-328
    • (1992) Calcolo , vol.29 , Issue.3-4 , pp. 313-328
    • Aimi, A.1    Diligenti, M.2
  • 9
    • 51249168794 scopus 로고
    • Error estimation in the computation of eigenvectors in the buckling problem for a plate embedded at the boundary
    • Aimi A., and Diligenti M. Error estimation in the computation of eigenvectors in the buckling problem for a plate embedded at the boundary. Calcolo 30 2 (1993) 171-187
    • (1993) Calcolo , vol.30 , Issue.2 , pp. 171-187
    • Aimi, A.1    Diligenti, M.2
  • 11
    • 26944461586 scopus 로고    scopus 로고
    • Inverse spectral theory for symmetric operators with several gaps: Scalar-type Weyl functions
    • Albeverio S., Brasche J.F., Malamud M.M., and Neidhardt H. Inverse spectral theory for symmetric operators with several gaps: Scalar-type Weyl functions. J. Funct. Anal. 228 (2005) 144-188
    • (2005) J. Funct. Anal. , vol.228 , pp. 144-188
    • Albeverio, S.1    Brasche, J.F.2    Malamud, M.M.3    Neidhardt, H.4
  • 12
    • 84961468935 scopus 로고
    • Point interactions in two dimensions: Basic properties, approximations and applications to solid state physics
    • Albeverio S., Gesztesy F., Høegh-Krohn R., and Holden H. Point interactions in two dimensions: Basic properties, approximations and applications to solid state physics. J. Reine Angew. Math. 380 (1987) 87-107
    • (1987) J. Reine Angew. Math. , vol.380 , pp. 87-107
    • Albeverio, S.1    Gesztesy, F.2    Høegh-Krohn, R.3    Holden, H.4
  • 14
    • 0002781662 scopus 로고
    • The Birman-Krein-Vishik theory of selfadjoint extensions of semibounded operators
    • Alonso A., and Simon B. The Birman-Krein-Vishik theory of selfadjoint extensions of semibounded operators. J. Operator Theory 4 (1980) 251-270
    • (1980) J. Operator Theory , vol.4 , pp. 251-270
    • Alonso, A.1    Simon, B.2
  • 15
    • 33646406768 scopus 로고
    • The Birman-Krein-Vishik theory of selfadjoint extensions of semibounded operators
    • (addenda)
    • Alonso A., and Simon B. The Birman-Krein-Vishik theory of selfadjoint extensions of semibounded operators. J. Operator Theory 6 (1981) 407 (addenda)
    • (1981) J. Operator Theory , vol.6 , pp. 407
    • Alonso, A.1    Simon, B.2
  • 16
    • 3042526641 scopus 로고    scopus 로고
    • M operators: A generalization of Weyl-Titchmarsh theory
    • Amrein W.O., and Pearson D.B. M operators: A generalization of Weyl-Titchmarsh theory. J. Comput. Appl. Math. 171 (2004) 1-26
    • (2004) J. Comput. Appl. Math. , vol.171 , pp. 1-26
    • Amrein, W.O.1    Pearson, D.B.2
  • 17
    • 30244548731 scopus 로고
    • Positive selfadjoint extensions of positive symmetric operators
    • Ando T., and Nishio K. Positive selfadjoint extensions of positive symmetric operators. Tohoku Math. J. (2) 22 (1970) 65-75
    • (1970) Tohoku Math. J. (2) , vol.22 , pp. 65-75
    • Ando, T.1    Nishio, K.2
  • 18
    • 16244400189 scopus 로고    scopus 로고
    • On m-accretive extensions and restrictions
    • Arlinskii Yu.M. On m-accretive extensions and restrictions. Methods Funct. Anal. Topology 4 (1998) 1-26
    • (1998) Methods Funct. Anal. Topology , vol.4 , pp. 1-26
    • Arlinskii, Yu.M.1
  • 19
    • 0038086984 scopus 로고    scopus 로고
    • Abstract boundary conditions for maximal sectorial extensions of sectorial operators
    • Arlinskii Yu.M. Abstract boundary conditions for maximal sectorial extensions of sectorial operators. Math. Nachr. 209 (2000) 5-36
    • (2000) Math. Nachr. , vol.209 , pp. 5-36
    • Arlinskii, Yu.M.1
  • 20
    • 0141952639 scopus 로고    scopus 로고
    • On the class of extremal extensions of a nonnegative operator
    • Recent Advances in Operator Theory and Related Topics. Kérchy L., Foias C., Gohberg I., and Langer H. (Eds), Birkhäuser, Basel
    • Arlinskii Yu.M., Hassi S., Sebestyén Z., and de Snoo H.S.V. On the class of extremal extensions of a nonnegative operator. In: Kérchy L., Foias C., Gohberg I., and Langer H. (Eds). Recent Advances in Operator Theory and Related Topics. Oper. Theory Adv. Appl. vol. 127 (2001), Birkhäuser, Basel 41-81
    • (2001) Oper. Theory Adv. Appl. , vol.127 , pp. 41-81
    • Arlinskii, Yu.M.1    Hassi, S.2    Sebestyén, Z.3    de Snoo, H.S.V.4
  • 21
    • 16244374670 scopus 로고    scopus 로고
    • On the theory of nonnegative selfadjoint extensions of a nonnegative symmetric operator
    • Arlinskii Yu.M., and Tsekanovskii E.R. On the theory of nonnegative selfadjoint extensions of a nonnegative symmetric operator. Rep. Nat. Acad. Sci. Ukraine 11 (2002) 30-37
    • (2002) Rep. Nat. Acad. Sci. Ukraine , vol.11 , pp. 30-37
    • Arlinskii, Yu.M.1    Tsekanovskii, E.R.2
  • 22
    • 0141976303 scopus 로고    scopus 로고
    • On von Neumann's problem in extension theory of nonnegative operators
    • Arlinskiǐ Yu.M., and Tsekanovskiǐ E.R. On von Neumann's problem in extension theory of nonnegative operators. Proc. Amer. Math. Soc. 131 (2003) 3143-3154
    • (2003) Proc. Amer. Math. Soc. , vol.131 , pp. 3143-3154
    • Arlinskiǐ, Yu.M.1    Tsekanovskiǐ, E.R.2
  • 24
    • 73749087488 scopus 로고    scopus 로고
    • M. Kreǐn's research on semibounded operators, its contemporary developments, and applications
    • Modern Analysis and Applications. The Mark Krein Centenary Conference, vol. 1. Adamyan V., Berezansky Y.M., Gohberg I., Gorbachuk M.L., Gorbachuk V., Kochubei A.N., Langer H., and Popov G. (Eds), Birkhäuser, Basel
    • Arlinskiǐ Yu., and Tsekanovskiǐ E. M. Kreǐn's research on semibounded operators, its contemporary developments, and applications. In: Adamyan V., Berezansky Y.M., Gohberg I., Gorbachuk M.L., Gorbachuk V., Kochubei A.N., Langer H., and Popov G. (Eds). Modern Analysis and Applications. The Mark Krein Centenary Conference, vol. 1. Oper. Theory Adv. Appl. vol. 190 (2009), Birkhäuser, Basel 65-114
    • (2009) Oper. Theory Adv. Appl. , vol.190 , pp. 65-114
    • Arlinskiǐ, Yu.1    Tsekanovskiǐ, E.2
  • 25
    • 0010423838 scopus 로고    scopus 로고
    • Isoperimetric and universal inequalities for eigenvalues
    • Spectral Theory and Geometry. Davies B., and Safarov Yu. (Eds), Cambridge Univ. Press, Cambridge
    • Ashbaugh M.S. Isoperimetric and universal inequalities for eigenvalues. In: Davies B., and Safarov Yu. (Eds). Spectral Theory and Geometry. London Math. Soc. Lecture Note Ser. vol. 273 (1999), Cambridge Univ. Press, Cambridge 95-139
    • (1999) London Math. Soc. Lecture Note Ser. , vol.273 , pp. 95-139
    • Ashbaugh, M.S.1
  • 26
    • 73749085057 scopus 로고    scopus 로고
    • On universal inequalities for the low eigenvalues of the buckling problem
    • Partial Differential Equations and Inverse Problems, Amer. Math. Soc., Providence, RI
    • Ashbaugh M.S. On universal inequalities for the low eigenvalues of the buckling problem. Partial Differential Equations and Inverse Problems. Contemp. Math. vol. 362 (2004), Amer. Math. Soc., Providence, RI 13-31
    • (2004) Contemp. Math. , vol.362 , pp. 13-31
    • Ashbaugh, M.S.1
  • 27
    • 73749086898 scopus 로고    scopus 로고
    • On universal inequalities for the low eigenvalues of the buckling problem II
    • preprint
    • M.S. Ashbaugh, On universal inequalities for the low eigenvalues of the buckling problem II, preprint, 2008
    • (2008)
    • Ashbaugh, M.S.1
  • 30
    • 73749088546 scopus 로고    scopus 로고
    • M.S. Ashbaugh, H.A. Levine, Inequalities for the Dirichlet and Neumann eigenvalues of the Laplacian for domains on spheres, in: Équations aux Dérivées Partielles, Saint-Jean-de-Monts, 1997, Exp. I, École Polytechnique, Palaiseau, 1997, 15 pp
    • M.S. Ashbaugh, H.A. Levine, Inequalities for the Dirichlet and Neumann eigenvalues of the Laplacian for domains on spheres, in: Équations aux Dérivées Partielles, Saint-Jean-de-Monts, 1997, Exp. I, École Polytechnique, Palaiseau, 1997, 15 pp
  • 31
    • 0000079935 scopus 로고
    • Symmetry theorems related to Pompeiu's problem
    • Aviles P. Symmetry theorems related to Pompeiu's problem. Amer. J. Math. 108 (1986) 1023-1036
    • (1986) Amer. J. Math. , vol.108 , pp. 1023-1036
    • Aviles, P.1
  • 32
    • 0001238188 scopus 로고
    • Continuous dependence of eigenvalues on the domain
    • Babuška I., and Výborný R. Continuous dependence of eigenvalues on the domain. Czechoslovak Math. J. 15 (1965) 169-178
    • (1965) Czechoslovak Math. J. , vol.15 , pp. 169-178
    • Babuška, I.1    Výborný, R.2
  • 33
    • 33846389763 scopus 로고    scopus 로고
    • Boundary value problems for partial differential operators on bounded domains
    • Behrndt J., and Langer M. Boundary value problems for partial differential operators on bounded domains. J. Funct. Anal. 243 (2007) 536-565
    • (2007) J. Funct. Anal. , vol.243 , pp. 536-565
    • Behrndt, J.1    Langer, M.2
  • 34
    • 0000146323 scopus 로고
    • On the theory of self-adjoint extensions of positive definite operators
    • (in Russian)
    • Birman M.Sh. On the theory of self-adjoint extensions of positive definite operators. Mat. Sb. 38 (1956) 431-450 (in Russian)
    • (1956) Mat. Sb. , vol.38 , pp. 431-450
    • Birman, M.Sh.1
  • 35
    • 11744251607 scopus 로고
    • Perturbations of the continuous spectrum of a singular elliptic operator by varying the boundary and the boundary conditions
    • (in Russian); Engl. transl.:
    • Birman M.Sh. Perturbations of the continuous spectrum of a singular elliptic operator by varying the boundary and the boundary conditions. Vestn. Leningrad Univ. 17 1 (1962) 22-55 (in Russian); Engl. transl.:
    • (1962) Vestn. Leningrad Univ. , vol.17 , Issue.1 , pp. 22-55
    • Birman, M.Sh.1
  • 36
    • 79956153395 scopus 로고    scopus 로고
    • Perturbations of the continuous spectrum of a singular elliptic operator by varying the boundary and the boundary conditions
    • Spectral Theory of Differential Operators: M.Sh. Birman 80th Anniversary Collection, in: Advances in the Mathematical Sciences, vol. 225. Suslina T., and Yafaev D. (Eds), Amer. Math. Soc., Providence, RI
    • Birman M.Sh. Perturbations of the continuous spectrum of a singular elliptic operator by varying the boundary and the boundary conditions. In: Suslina T., and Yafaev D. (Eds). Spectral Theory of Differential Operators: M.Sh. Birman 80th Anniversary Collection, in: Advances in the Mathematical Sciences, vol. 225. Amer. Math. Soc. Transl. Ser. 2 vol. 2 (2008), Amer. Math. Soc., Providence, RI 19-53
    • (2008) Amer. Math. Soc. Transl. Ser. 2 , vol.2 , pp. 19-53
    • Birman, M.Sh.1
  • 37
    • 73749084470 scopus 로고    scopus 로고
    • Weyl asymptotics of the spectrum of the Maxwell operator with non-smooth coefficients in Lipschitz domains
    • Nonlinear Equations and Spectral Theory, Amer. Math. Soc., Providence, RI
    • Birman M.S., and Filonov N.D. Weyl asymptotics of the spectrum of the Maxwell operator with non-smooth coefficients in Lipschitz domains. Nonlinear Equations and Spectral Theory. Amer. Math. Soc. Transl. Ser. 2 vol. 220 (2007), Amer. Math. Soc., Providence, RI 27-44
    • (2007) Amer. Math. Soc. Transl. Ser. 2 , vol.220 , pp. 27-44
    • Birman, M.S.1    Filonov, N.D.2
  • 38
    • 0010568866 scopus 로고
    • Leading term in the asymptotic spectral formula for "non-smooth" elliptic problems
    • (in Russian); Engl. transl.:
    • Birman M.Sh., and Solomyak M.Z. Leading term in the asymptotic spectral formula for "non-smooth" elliptic problems. Funktsional. Anal. i Prilozhen. 4 4 (1970) 1-13 (in Russian); Engl. transl.:
    • (1970) Funktsional. Anal. i Prilozhen. , vol.4 , Issue.4 , pp. 1-13
    • Birman, M.Sh.1    Solomyak, M.Z.2
  • 39
    • 0010568866 scopus 로고
    • Leading term in the asymptotic spectral formula for "non-smooth" elliptic problems
    • Birman M.Sh., and Solomyak M.Z. Leading term in the asymptotic spectral formula for "non-smooth" elliptic problems. Funct. Anal. Appl. 4 (1970) 265-275
    • (1970) Funct. Anal. Appl. , vol.4 , pp. 265-275
    • Birman, M.Sh.1    Solomyak, M.Z.2
  • 40
    • 34250470624 scopus 로고
    • On the asymptotic spectrum of "non-smooth" elliptic equations
    • (in Russian); Engl. transl.:
    • Birman M.Sh., and Solomyak M.Z. On the asymptotic spectrum of "non-smooth" elliptic equations. Funktsional. Anal. i Prilozhen. 5 1 (1971) 69-70 (in Russian); Engl. transl.:
    • (1971) Funktsional. Anal. i Prilozhen. , vol.5 , Issue.1 , pp. 69-70
    • Birman, M.Sh.1    Solomyak, M.Z.2
  • 41
    • 34250470624 scopus 로고
    • On the asymptotic spectrum of "non-smooth" elliptic equations
    • Birman M.Sh., and Solomyak M.Z. On the asymptotic spectrum of "non-smooth" elliptic equations. Funct. Anal. Appl. 5 (1971) 56-57
    • (1971) Funct. Anal. Appl. , vol.5 , pp. 56-57
    • Birman, M.Sh.1    Solomyak, M.Z.2
  • 42
    • 0002920462 scopus 로고
    • Spectral asymptotics of nonsmooth elliptic operators. I
    • Birman M.S., and Solomjak M.Z. Spectral asymptotics of nonsmooth elliptic operators. I. Trans. Moscow Math. Soc. 27 (1972) 1-52
    • (1972) Trans. Moscow Math. Soc. , vol.27 , pp. 1-52
    • Birman, M.S.1    Solomjak, M.Z.2
  • 43
    • 0002920462 scopus 로고
    • Spectral asymptotics of nonsmooth elliptic operators. I
    • Birman M.S., and Solomjak M.Z. Spectral asymptotics of nonsmooth elliptic operators. I. Trans. Moscow Math. Soc. 28 (1973) 1-32
    • (1973) Trans. Moscow Math. Soc. , vol.28 , pp. 1-32
    • Birman, M.S.1    Solomjak, M.Z.2
  • 44
    • 0010657113 scopus 로고
    • Asymptotic behavior of the spectrum of differential equations
    • (in Russian); Engl. transl.:
    • Birman M.Sh., and Solomyak M.Z. Asymptotic behavior of the spectrum of differential equations. Itogi Nauki i Tekhniki Matemat. Anal. 14 (1977) 5-58 (in Russian); Engl. transl.:
    • (1977) Itogi Nauki i Tekhniki Matemat. Anal. , vol.14 , pp. 5-58
    • Birman, M.Sh.1    Solomyak, M.Z.2
  • 45
    • 0001212044 scopus 로고
    • Asymptotic behavior of the spectrum of differential equations
    • Birman M.Sh., and Solomyak M.Z. Asymptotic behavior of the spectrum of differential equations. J. Soviet Math. 12 3 (1979) 247-283
    • (1979) J. Soviet Math. , vol.12 , Issue.3 , pp. 247-283
    • Birman, M.Sh.1    Solomyak, M.Z.2
  • 46
    • 0242505464 scopus 로고
    • Weyl asymptotics of the spectrum of the Maxwell operator for domains with a Lipschitz boundary
    • (in Russian)
    • Birman M.S., and Solomjak M.Z. Weyl asymptotics of the spectrum of the Maxwell operator for domains with a Lipschitz boundary. Vestn. Leningrad. Univ. Mat. Mekh. Astronom. 127 3 (1987) 23-28 (in Russian)
    • (1987) Vestn. Leningrad. Univ. Mat. Mekh. Astronom. , vol.127 , Issue.3 , pp. 23-28
    • Birman, M.S.1    Solomjak, M.Z.2
  • 47
    • 0033294470 scopus 로고    scopus 로고
    • High precision solutions of two fourth order eigenvalue problems
    • Bjørstad P.E., and Tjøstheim B.P. High precision solutions of two fourth order eigenvalue problems. Computing 63 2 (1999) 97-107
    • (1999) Computing , vol.63 , Issue.2 , pp. 97-107
    • Bjørstad, P.E.1    Tjøstheim, B.P.2
  • 48
    • 73749086656 scopus 로고
    • Pointwise bounds in the first biharmonic boundary value problem
    • Bramble J.H., and Payne L.E. Pointwise bounds in the first biharmonic boundary value problem. J. Math. Phys. 42 (1963) 278-286
    • (1963) J. Math. Phys. , vol.42 , pp. 278-286
    • Bramble, J.H.1    Payne, L.E.2
  • 50
    • 20844450747 scopus 로고    scopus 로고
    • On the Krein and Friedrichs extension of a positive Jacobi operator
    • Brown B.M., and Christiansen J.S. On the Krein and Friedrichs extension of a positive Jacobi operator. Expo. Math. 23 (2005) 179-186
    • (2005) Expo. Math. , vol.23 , pp. 179-186
    • Brown, B.M.1    Christiansen, J.S.2
  • 51
    • 67449113919 scopus 로고    scopus 로고
    • M-functions for closed extensions of adjoint pairs of operators with applications to elliptic boundary problems
    • Brown B.M., Grubb G., and Wood I.G. M-functions for closed extensions of adjoint pairs of operators with applications to elliptic boundary problems. Math. Nachr. 282 (2009) 314-347
    • (2009) Math. Nachr. , vol.282 , pp. 314-347
    • Brown, B.M.1    Grubb, G.2    Wood, I.G.3
  • 52
    • 62949213710 scopus 로고    scopus 로고
    • The abstract Titchmarsh-Weyl M-function for adjoint operator pairs and its relation to the spectrum
    • Brown M., Hinchcliffe J., Marletta M., Naboko S., and Wood I. The abstract Titchmarsh-Weyl M-function for adjoint operator pairs and its relation to the spectrum. Integral Equations Operator Theory 63 (2009) 297-320
    • (2009) Integral Equations Operator Theory , vol.63 , pp. 297-320
    • Brown, M.1    Hinchcliffe, J.2    Marletta, M.3    Naboko, S.4    Wood, I.5
  • 53
    • 44649199294 scopus 로고    scopus 로고
    • Boundary triplets and M-functions for non-selfadjoint operators, with applications to elliptic PDEs and block operator matrices
    • Brown M., Marletta M., Naboko S., and Wood I. Boundary triplets and M-functions for non-selfadjoint operators, with applications to elliptic PDEs and block operator matrices. J. London Math. Soc. (2) 77 (2008) 700-718
    • (2008) J. London Math. Soc. (2) , vol.77 , pp. 700-718
    • Brown, M.1    Marletta, M.2    Naboko, S.3    Wood, I.4
  • 54
    • 41849098938 scopus 로고    scopus 로고
    • Spectra of self-adjoint extensions and applications to solvable Schrödinger operators
    • Brüning J., Geyler V., and Pankrashkin K. Spectra of self-adjoint extensions and applications to solvable Schrödinger operators. Rev. Math. Phys. 20 (2008) 1-70
    • (2008) Rev. Math. Phys. , vol.20 , pp. 1-70
    • Brüning, J.1    Geyler, V.2    Pankrashkin, K.3
  • 55
    • 36549103480 scopus 로고
    • Deficiency indices and singular boundary conditions in quantum mechanics
    • Bulla W., and Gesztesy F. Deficiency indices and singular boundary conditions in quantum mechanics. J. Math. Phys. 26 (1985) 2520-2528
    • (1985) J. Math. Phys. , vol.26 , pp. 2520-2528
    • Bulla, W.1    Gesztesy, F.2
  • 56
    • 39749158441 scopus 로고    scopus 로고
    • Spectral stability of Dirichlet second order uniformly elliptic operators
    • Burenkov V.I., and Lamberti P.D. Spectral stability of Dirichlet second order uniformly elliptic operators. J. Differential Equations 244 (2008) 1712-1740
    • (2008) J. Differential Equations , vol.244 , pp. 1712-1740
    • Burenkov, V.I.1    Lamberti, P.D.2
  • 58
    • 33747101034 scopus 로고
    • On the search for the asymptotic behaviour of the eigenvalues of the Dirichlet Laplacian for bounded irregular domains
    • Some Aspects of Fractals in Mathematics and Physics. Toulouse, 1993
    • Caetano A.M. On the search for the asymptotic behaviour of the eigenvalues of the Dirichlet Laplacian for bounded irregular domains. Some Aspects of Fractals in Mathematics and Physics. Toulouse, 1993. Internat. J. Appl. Sci. Comput. 2 2 (1995) 261-287
    • (1995) Internat. J. Appl. Sci. Comput. , vol.2 , Issue.2 , pp. 261-287
    • Caetano, A.M.1
  • 59
    • 5044240616 scopus 로고    scopus 로고
    • Eigenvalue asymptotics of the Stokes operator for fractal domains
    • Caetano A.M. Eigenvalue asymptotics of the Stokes operator for fractal domains. Proc. London Math. Soc. (3) 76 3 (1998) 579-602
    • (1998) Proc. London Math. Soc. (3) , vol.76 , Issue.3 , pp. 579-602
    • Caetano, A.M.1
  • 60
    • 0003315989 scopus 로고
    • Selected Problems on Exceptional Sets
    • Princeton
    • Carleson L. Selected Problems on Exceptional Sets. Van Nostrand Mathematical Studies vol. 13 (1967), Princeton
    • (1967) Van Nostrand Mathematical Studies , vol.13
    • Carleson, L.1
  • 61
    • 31744445275 scopus 로고    scopus 로고
    • Universal bounds for eigenvalues of a buckling problem
    • Cheng Q.-M., and Yang H. Universal bounds for eigenvalues of a buckling problem. Comm. Math. Phys. 262 (2006) 663-675
    • (2006) Comm. Math. Phys. , vol.262 , pp. 663-675
    • Cheng, Q.-M.1    Yang, H.2
  • 62
    • 0037373697 scopus 로고    scopus 로고
    • Dirichlet problems on varying domains
    • Daners D. Dirichlet problems on varying domains. J. Differential Equations 188 (2003) 591-624
    • (2003) J. Differential Equations , vol.188 , pp. 591-624
    • Daners, D.1
  • 63
    • 0031227261 scopus 로고    scopus 로고
    • p spectral theory of higher-order elliptic differential operators
    • p spectral theory of higher-order elliptic differential operators. Bull. London Math. Soc. 29 5 (1997) 513-546
    • (1997) Bull. London Math. Soc. , vol.29 , Issue.5 , pp. 513-546
    • Davies, E.B.1
  • 65
    • 0002179607 scopus 로고
    • Generalized resolvents and the boundary value problems for Hermitian operators with gaps
    • Derkach V.A., and Malamud M.M. Generalized resolvents and the boundary value problems for Hermitian operators with gaps. J. Funct. Anal. 95 (1991) 1-95
    • (1991) J. Funct. Anal. , vol.95 , pp. 1-95
    • Derkach, V.A.1    Malamud, M.M.2
  • 66
    • 0000530485 scopus 로고
    • The extension theory of Hermitian operators and the moment problem
    • Derkach V.A., and Malamud M.M. The extension theory of Hermitian operators and the moment problem. J. Math. Sci. 73 (1995) 141-242
    • (1995) J. Math. Sci. , vol.73 , pp. 141-242
    • Derkach, V.A.1    Malamud, M.M.2
  • 67
    • 0041133541 scopus 로고
    • Sectorial extensions of a positive operator and the characteristic function
    • Derkach V.A., Malamud M.M., and Tsekanovskii E.R. Sectorial extensions of a positive operator and the characteristic function. Soviet Math. Dokl. 37 (1988) 106-110
    • (1988) Soviet Math. Dokl. , vol.37 , pp. 106-110
    • Derkach, V.A.1    Malamud, M.M.2    Tsekanovskii, E.R.3
  • 68
    • 34249957100 scopus 로고
    • Sectorial extensions of a positive operator and the characteristic function
    • Derkach V.A., Malamud M.M., and Tsekanovskii E.R. Sectorial extensions of a positive operator and the characteristic function. Ukrainian Math. J. 41 (1989) 136-142
    • (1989) Ukrainian Math. J. , vol.41 , pp. 136-142
    • Derkach, V.A.1    Malamud, M.M.2    Tsekanovskii, E.R.3
  • 69
    • 0003418183 scopus 로고
    • Birkhäuser, Boston translated by F. Flaherty from the second Portuguese edition
    • do Carmo M.P. Riemannian Geometry (1992), Birkhäuser, Boston translated by F. Flaherty from the second Portuguese edition
    • (1992) Riemannian Geometry
    • do Carmo, M.P.1
  • 70
    • 84981761432 scopus 로고
    • On the perturbation of spectra
    • Donoghue W.F. On the perturbation of spectra. Comm. Pure Appl. Math. 18 (1965) 559-579
    • (1965) Comm. Pure Appl. Math. , vol.18 , pp. 559-579
    • Donoghue, W.F.1
  • 72
    • 25844453385 scopus 로고    scopus 로고
    • Complex symplectic spaces and boundary value problems
    • Everitt W.N., and Markus L. Complex symplectic spaces and boundary value problems. Bull. Amer. Math. Soc. (N.S.) 42 (2005) 461-500
    • (2005) Bull. Amer. Math. Soc. (N.S.) , vol.42 , pp. 461-500
    • Everitt, W.N.1    Markus, L.2
  • 73
    • 16244404682 scopus 로고    scopus 로고
    • An unusual self-adjoint linear partial differential operator
    • Everitt W.N., Markus L., and Plum M. An unusual self-adjoint linear partial differential operator. Trans. Amer. Math. Soc. 357 (2004) 1303-1324
    • (2004) Trans. Amer. Math. Soc. , vol.357 , pp. 1303-1324
    • Everitt, W.N.1    Markus, L.2    Plum, M.3
  • 74
    • 34547578883 scopus 로고    scopus 로고
    • A continuum of unusual self-adjoint linear partial differential operators
    • Everitt W.N., Markus L., Muzzulini M., and Plum M. A continuum of unusual self-adjoint linear partial differential operators. J. Comput. Appl. Math. 208 (2007) 164-175
    • (2007) J. Comput. Appl. Math. , vol.208 , pp. 164-175
    • Everitt, W.N.1    Markus, L.2    Muzzulini, M.3    Plum, M.4
  • 75
    • 0003272522 scopus 로고
    • Self-Adjoint Operators
    • Springer, Berlin
    • Faris W.G. Self-Adjoint Operators. Lecture Notes in Math. vol. 433 (1975), Springer, Berlin
    • (1975) Lecture Notes in Math. , vol.433
    • Faris, W.G.1
  • 76
    • 16244379899 scopus 로고
    • Über die Friedrichsche Fortsetzung halbbeschränkter Hermitescher Operatoren
    • Freudenthal H. Über die Friedrichsche Fortsetzung halbbeschränkter Hermitescher Operatoren. Kon. Akad. Wetensch. Amsterdam Proc. 39 (1936) 832-833
    • (1936) Kon. Akad. Wetensch. Amsterdam Proc. , vol.39 , pp. 832-833
    • Freudenthal, H.1
  • 77
    • 34250953136 scopus 로고
    • Spektraltheorie halbeschränkter Operatoren und Anwendung auf die Spektralzerlegung von Differentialoperatoren I, II
    • 685-713
    • Friedrichs K. Spektraltheorie halbeschränkter Operatoren und Anwendung auf die Spektralzerlegung von Differentialoperatoren I, II. Math. Ann. 109 (1934) 465-487 685-713
    • (1934) Math. Ann. , vol.109 , pp. 465-487
    • Friedrichs, K.1
  • 78
    • 34250963179 scopus 로고
    • Spektraltheorie halbeschränkter Operatoren und Anwendung auf die Spektralzerlegung von Differentialoperatoren I, II
    • Friedrichs K. Spektraltheorie halbeschränkter Operatoren und Anwendung auf die Spektralzerlegung von Differentialoperatoren I, II. Math. Ann. 110 (1935) 777-779
    • (1935) Math. Ann. , vol.110 , pp. 777-779
    • Friedrichs, K.1
  • 79
    • 0011763835 scopus 로고    scopus 로고
    • Continuous domain dependence of the eigenvalues of the Dirichlet Laplacian and related operators in Hilbert space
    • Fuglede B. Continuous domain dependence of the eigenvalues of the Dirichlet Laplacian and related operators in Hilbert space. J. Funct. Anal. 167 (1999) 183-200
    • (1999) J. Funct. Anal. , vol.167 , pp. 183-200
    • Fuglede, B.1
  • 82
    • 0000921973 scopus 로고    scopus 로고
    • Some applications of operator-valued Herglotz functions
    • Operator Theory, System Theory and Related Topics, Birkhäuser, Basel
    • Gesztesy F., Kalton N.J., Makarov K.A., and Tsekanovskii E. Some applications of operator-valued Herglotz functions. Operator Theory, System Theory and Related Topics. Oper. Theory Adv. Appl. vol. 123 (2001), Birkhäuser, Basel 271-321
    • (2001) Oper. Theory Adv. Appl. , vol.123 , pp. 271-321
    • Gesztesy, F.1    Kalton, N.J.2    Makarov, K.A.3    Tsekanovskii, E.4
  • 83
    • 29144485504 scopus 로고    scopus 로고
    • Nonselfadjoint operators, infinite determinants, and some applications
    • Gesztesy F., Latushkin Y., Mitrea M., and Zinchenko M. Nonselfadjoint operators, infinite determinants, and some applications. Russ. J. Math. Phys. 12 (2005) 443-471
    • (2005) Russ. J. Math. Phys. , vol.12 , pp. 443-471
    • Gesztesy, F.1    Latushkin, Y.2    Mitrea, M.3    Zinchenko, M.4
  • 85
    • 67650045066 scopus 로고    scopus 로고
    • Generalized Robin boundary conditions, Robin-to-Dirichlet maps, and Krein-type resolvent formulas for Schrödinger operators on bounded Lipschitz domains
    • Perspectives in Partial Differential Equations, Harmonic Analysis and Applications: A Volume in Honor of Vladimir G. Maz'ya's 70th Birthday. Mitrea D., and Mitrea M. (Eds), Amer. Math. Soc., Providence, RI
    • Gesztesy F., and Mitrea M. Generalized Robin boundary conditions, Robin-to-Dirichlet maps, and Krein-type resolvent formulas for Schrödinger operators on bounded Lipschitz domains. In: Mitrea D., and Mitrea M. (Eds). Perspectives in Partial Differential Equations, Harmonic Analysis and Applications: A Volume in Honor of Vladimir G. Maz'ya's 70th Birthday. Proc. Sympos. Pure Math. vol. 79 (2008), Amer. Math. Soc., Providence, RI 105-173
    • (2008) Proc. Sympos. Pure Math. , vol.79 , pp. 105-173
    • Gesztesy, F.1    Mitrea, M.2
  • 86
    • 67650073688 scopus 로고    scopus 로고
    • Robin-to-Robin maps and Krein-type resolvent formulas for Schrödinger operators on bounded Lipschitz domains
    • Modern Analysis and Applications. The Mark Krein Centenary Conference, vol. 2. Adamyan V., Berezansky Y.M., Gohberg I., Gorbachuk M.L., Gorbachuk V., Kochubei A.N., Langer H., and Popov G. (Eds), Birkhäuser, Basel
    • Gesztesy F., and Mitrea M. Robin-to-Robin maps and Krein-type resolvent formulas for Schrödinger operators on bounded Lipschitz domains. In: Adamyan V., Berezansky Y.M., Gohberg I., Gorbachuk M.L., Gorbachuk V., Kochubei A.N., Langer H., and Popov G. (Eds). Modern Analysis and Applications. The Mark Krein Centenary Conference, vol. 2. Oper. Theory Adv. Appl. vol. 191 (2009), Birkhäuser, Basel 81-113
    • (2009) Oper. Theory Adv. Appl. , vol.191 , pp. 81-113
    • Gesztesy, F.1    Mitrea, M.2
  • 87
    • 70249086895 scopus 로고    scopus 로고
    • Generalized Robin Laplacians and some remarks on a paper by Filonov on eigenvalue inequalities
    • Gesztesy F., and Mitrea M. Generalized Robin Laplacians and some remarks on a paper by Filonov on eigenvalue inequalities. J. Differential Equations 247 (2009) 2871-2896
    • (2009) J. Differential Equations , vol.247 , pp. 2871-2896
    • Gesztesy, F.1    Mitrea, M.2
  • 88
    • 73749086042 scopus 로고    scopus 로고
    • Self-adjoint extensions of the Laplacian and Krein-type resolvent formulas in nonsmooth domains
    • preprint, arXiv:0907.1750
    • F. Gesztesy, M. Mitrea, Self-adjoint extensions of the Laplacian and Krein-type resolvent formulas in nonsmooth domains, preprint, arXiv:0907.1750, 2009
    • (2009)
    • Gesztesy, F.1    Mitrea, M.2
  • 89
  • 90
    • 0002894574 scopus 로고    scopus 로고
    • On matrix-valued Herglotz functions
    • Gesztesy F., and Tsekanovskii E. On matrix-valued Herglotz functions. Math. Nachr. 218 (2000) 61-138
    • (2000) Math. Nachr. , vol.218 , pp. 61-138
    • Gesztesy, F.1    Tsekanovskii, E.2
  • 93
    • 33846394145 scopus 로고
    • A characterization of the non-local boundary value problems associated with an elliptic operator
    • Grubb G. A characterization of the non-local boundary value problems associated with an elliptic operator. Ann. Sc. Norm. Super. Pisa Cl. Sci. (3) 22 (1968) 425-513
    • (1968) Ann. Sc. Norm. Super. Pisa Cl. Sci. (3) , vol.22 , pp. 425-513
    • Grubb, G.1
  • 94
    • 73749086527 scopus 로고
    • Les problèmes aux limites généraux d'un opérateur elliptique, provenant de le théorie variationnelle
    • Grubb G. Les problèmes aux limites généraux d'un opérateur elliptique, provenant de le théorie variationnelle. Bull. Sci. Math. (2) 94 (1970) 113-157
    • (1970) Bull. Sci. Math. (2) , vol.94 , pp. 113-157
    • Grubb, G.1
  • 95
    • 2542440111 scopus 로고
    • Spectral asymptotics for the "soft" selfadjoint extension of a symmetric elliptic differential operator
    • Grubb G. Spectral asymptotics for the "soft" selfadjoint extension of a symmetric elliptic differential operator. J. Operator Theory 10 (1983) 9-20
    • (1983) J. Operator Theory , vol.10 , pp. 9-20
    • Grubb, G.1
  • 96
    • 33646431703 scopus 로고    scopus 로고
    • Known and unknown results on elliptic boundary problems
    • Grubb G. Known and unknown results on elliptic boundary problems. Bull. Amer. Math. Soc. (N.S.) 43 (2006) 227-230
    • (2006) Bull. Amer. Math. Soc. (N.S.) , vol.43 , pp. 227-230
    • Grubb, G.1
  • 97
    • 67650957737 scopus 로고    scopus 로고
    • Krein resolvent formulas for elliptic boundary problems in nonsmooth domains
    • Grubb G. Krein resolvent formulas for elliptic boundary problems in nonsmooth domains. Rend. Sem. Mat. Univ. Pol. Torino 66 (2008) 271-297
    • (2008) Rend. Sem. Mat. Univ. Pol. Torino , vol.66 , pp. 271-297
    • Grubb, G.1
  • 98
    • 67650872475 scopus 로고    scopus 로고
    • Distributions and Operators
    • Springer, New York
    • Grubb G. Distributions and Operators. Grad. Texts in Math. vol. 252 (2009), Springer, New York
    • (2009) Grad. Texts in Math. , vol.252
    • Grubb, G.1
  • 99
    • 73749083781 scopus 로고
    • Perturbation of spectra and Krein extensions
    • Hartman P. Perturbation of spectra and Krein extensions. Rend. Circ. Mat. Palermo (2) 5 (1957) 341-354
    • (1957) Rend. Circ. Mat. Palermo (2) , vol.5 , pp. 341-354
    • Hartman, P.1
  • 100
    • 0040399696 scopus 로고
    • A notion of capacity which characterizes removable singularities
    • Harvey R., and Polking J.C. A notion of capacity which characterizes removable singularities. Trans. Amer. Math. Soc. 169 (1972) 183-195
    • (1972) Trans. Amer. Math. Soc. , vol.169 , pp. 183-195
    • Harvey, R.1    Polking, J.C.2
  • 101
    • 58149097461 scopus 로고    scopus 로고
    • On symmetries in the theory of finite rank singular perturbations
    • Hassi S., and Kuzhel S. On symmetries in the theory of finite rank singular perturbations. J. Funct. Anal. 256 (2009) 777-809
    • (2009) J. Funct. Anal. , vol.256 , pp. 777-809
    • Hassi, S.1    Kuzhel, S.2
  • 102
    • 7444232462 scopus 로고    scopus 로고
    • On Kreǐn's extension theory of nonnegative operators
    • Hassi S., Malamud M., and de Snoo H. On Kreǐn's extension theory of nonnegative operators. Math. Nachr. 274-275 (2004) 40-73
    • (2004) Math. Nachr. , vol.274-275 , pp. 40-73
    • Hassi, S.1    Malamud, M.2    de Snoo, H.3
  • 103
    • 42149103880 scopus 로고    scopus 로고
    • A general factorization approach to the extension theory of nonnegative operators and relations
    • Hassi S., Sandovici A., de Snoo H., and Winkler H. A general factorization approach to the extension theory of nonnegative operators and relations. J. Operator Theory 58 (2007) 351-386
    • (2007) J. Operator Theory , vol.58 , pp. 351-386
    • Hassi, S.1    Sandovici, A.2    de Snoo, H.3    Winkler, H.4
  • 104
    • 0039993368 scopus 로고    scopus 로고
    • Generalized Minkowski content, spectrum of fractal drums, fractal strings and the Riemann zeta-function
    • He C., and Lapidus M.L. Generalized Minkowski content, spectrum of fractal drums, fractal strings and the Riemann zeta-function. Mem. Amer. Math. Soc. 127 608 (1997)
    • (1997) Mem. Amer. Math. Soc. , vol.127 , Issue.608
    • He, C.1    Lapidus, M.L.2
  • 105
    • 84972557166 scopus 로고
    • Inequalities for eigenvalues of the biharmonic operator
    • Hile G.N., and Yeh R.Z. Inequalities for eigenvalues of the biharmonic operator. Pacific J. Math. 112 1 (1984) 115-133
    • (1984) Pacific J. Math. , vol.112 , Issue.1 , pp. 115-133
    • Hile, G.N.1    Yeh, R.Z.2
  • 106
    • 73749087832 scopus 로고
    • Bounds for the fundamental frequencies of an elastic medium
    • Hook S.M. Bounds for the fundamental frequencies of an elastic medium. Michigan Math. J. 38 (1991) 3-12
    • (1991) Michigan Math. J. , vol.38 , pp. 3-12
    • Hook, S.M.1
  • 107
    • 0000271720 scopus 로고
    • The inhomogeneous Dirichlet problem in Lipschitz domains
    • Jerison D., and Kenig C. The inhomogeneous Dirichlet problem in Lipschitz domains. J. Funct. Anal. 130 (1995) 161-219
    • (1995) J. Funct. Anal. , vol.130 , pp. 161-219
    • Jerison, D.1    Kenig, C.2
  • 109
    • 21144477675 scopus 로고
    • Buckling eigenvalue for a clamped plate embedded in an elastic medium and related questions
    • Kawohl B., Levine H.A., and Velte W. Buckling eigenvalue for a clamped plate embedded in an elastic medium and related questions. SIAM J. Math. Anal. 24 (1993) 327-340
    • (1993) SIAM J. Math. Anal. , vol.24 , pp. 327-340
    • Kawohl, B.1    Levine, H.A.2    Velte, W.3
  • 110
    • 73749084610 scopus 로고
    • Estimation of the remainder in a formula for the asymptotic behavior of the spectrum of nonsemibounded elliptic systems
    • (in Russian)
    • Kozlov V.A. Estimation of the remainder in a formula for the asymptotic behavior of the spectrum of nonsemibounded elliptic systems. Vestnik Leningrad. Univ. Mat. Mekh. Astronom. 125 4 (1979) 112-113 (in Russian)
    • (1979) Vestnik Leningrad. Univ. Mat. Mekh. Astronom. , vol.125 , Issue.4 , pp. 112-113
    • Kozlov, V.A.1
  • 111
    • 34250142619 scopus 로고
    • Estimates of the remainder in formulas for the asymptotic behavior of the spectrum for linear operator bundles
    • Engl. transl.:
    • Kozlov V.A. Estimates of the remainder in formulas for the asymptotic behavior of the spectrum for linear operator bundles. Funktsional. Anal. i Prilozhen. 17 2 (1983) 80-81 Engl. transl.:
    • (1983) Funktsional. Anal. i Prilozhen. , vol.17 , Issue.2 , pp. 80-81
    • Kozlov, V.A.1
  • 112
    • 34250142619 scopus 로고
    • Estimates of the remainder in formulas for the asymptotic behavior of the spectrum for linear operator bundles
    • Kozlov V.A. Estimates of the remainder in formulas for the asymptotic behavior of the spectrum for linear operator bundles. Funct. Anal. Appl. 17 2 (1983) 147-149
    • (1983) Funct. Anal. Appl. , vol.17 , Issue.2 , pp. 147-149
    • Kozlov, V.A.1
  • 113
    • 73749086093 scopus 로고
    • Remainder estimates in spectral asymptotic formulas for linear operator pencils
    • Linear and Nonlinear Partial Differential Equations. Spectral Asymptotic Behavior, Leningrad Univ., Leningrad Engl. transl.:
    • Kozlov V.A. Remainder estimates in spectral asymptotic formulas for linear operator pencils. Linear and Nonlinear Partial Differential Equations. Spectral Asymptotic Behavior. Probl. Mat. Anal. vol. 9 (1984), Leningrad Univ., Leningrad 34-56 Engl. transl.:
    • (1984) Probl. Mat. Anal. , vol.9 , pp. 34-56
    • Kozlov, V.A.1
  • 114
    • 34250131371 scopus 로고
    • Remainder estimates in spectral asymptotic formulas for linear operator pencils
    • Kozlov V.A. Remainder estimates in spectral asymptotic formulas for linear operator pencils. J. Sov. Math. 35 (1986) 2180-2193
    • (1986) J. Sov. Math. , vol.35 , pp. 2180-2193
    • Kozlov, V.A.1
  • 115
    • 0001467759 scopus 로고
    • On sign variation and the absence of "strong" zeros of solutions of elliptic equations
    • Kozlov V.A., Kondrat'ev V.A., and Maz'ya V.G. On sign variation and the absence of "strong" zeros of solutions of elliptic equations. Math. USSR Izv. 34 (1990) 337-353
    • (1990) Math. USSR Izv. , vol.34 , pp. 337-353
    • Kozlov, V.A.1    Kondrat'ev, V.A.2    Maz'ya, V.G.3
  • 116
    • 0002701051 scopus 로고
    • Über Minimaleigenschaften der Kugel in drei und mehr Dimensionen
    • Krahn E. Über Minimaleigenschaften der Kugel in drei und mehr Dimensionen. Acta Comment. Univ. Tartu. (Dorpat) A 9 (1926) 1-44
    • (1926) Acta Comment. Univ. Tartu. (Dorpat) A , vol.9 , pp. 1-44
    • Krahn, E.1
  • 118
    • 0000346864 scopus 로고
    • The theory of self-adjoint extensions of semi-bounded Hermitian transformations and its applications. I
    • (in Russian)
    • Krein M.G. The theory of self-adjoint extensions of semi-bounded Hermitian transformations and its applications. I. Mat. Sb. 20 (1947) 431-495 (in Russian)
    • (1947) Mat. Sb. , vol.20 , pp. 431-495
    • Krein, M.G.1
  • 119
    • 0000346863 scopus 로고
    • The theory of self-adjoint extensions of semi-bounded Hermitian transformations and its applications. II
    • (in Russian)
    • Krein M.G. The theory of self-adjoint extensions of semi-bounded Hermitian transformations and its applications. II. Mat. Sb. 21 (1947) 365-404 (in Russian)
    • (1947) Mat. Sb. , vol.21 , pp. 365-404
    • Krein, M.G.1
  • 120
    • 0041038047 scopus 로고
    • Q-functions and sc-resolvents of nondensely defined hermitian contractions
    • Krein M.G., and Ovcharenko I.E. Q-functions and sc-resolvents of nondensely defined hermitian contractions. Siberian Math. J. 18 (1977) 728-746
    • (1977) Siberian Math. J. , vol.18 , pp. 728-746
    • Krein, M.G.1    Ovcharenko, I.E.2
  • 121
    • 0040539526 scopus 로고
    • Inverse problems for Q-functions and resolvent matrices of positive hermitian operators
    • Krein M.G., and Ovčarenko I.E. Inverse problems for Q-functions and resolvent matrices of positive hermitian operators. Sovrem. Math. Dokl. 19 (1978) 1131-1134
    • (1978) Sovrem. Math. Dokl. , vol.19 , pp. 1131-1134
    • Krein, M.G.1    Ovčarenko, I.E.2
  • 123
    • 34250134102 scopus 로고
    • Distribution of eigenvalues of systems of the form A u = t B u
    • Levendorskii S.Z. Distribution of eigenvalues of systems of the form A u = t B u. Funct. Anal. Appl. 17 (1983) 149-151
    • (1983) Funct. Anal. Appl. , vol.17 , pp. 149-151
    • Levendorskii, S.Z.1
  • 124
    • 73749088703 scopus 로고
    • Asymptotics of the spectrum of linear operator pencils
    • Levendorskiǐ S.Z. Asymptotics of the spectrum of linear operator pencils. Math. USSR Sbornik 52 (1985) 245-266
    • (1985) Math. USSR Sbornik , vol.52 , pp. 245-266
    • Levendorskiǐ, S.Z.1
  • 125
    • 0021976070 scopus 로고
    • Unrestricted lower bounds for eigenvalues for classes of elliptic equations and systems of equations with applications to problems in elasticity
    • Levine H.A., and Protter M.H. Unrestricted lower bounds for eigenvalues for classes of elliptic equations and systems of equations with applications to problems in elasticity. Math. Methods Appl. Sci. 7 (1985) 210-222
    • (1985) Math. Methods Appl. Sci. , vol.7 , pp. 210-222
    • Levine, H.A.1    Protter, M.H.2
  • 126
    • 0041114598 scopus 로고
    • Inequalities between Dirichlet and Neumann eigenvalues
    • Levine H.A., and Weinberger H.F. Inequalities between Dirichlet and Neumann eigenvalues. Arch. Ration. Mech. Anal. 94 (1986) 193-208
    • (1986) Arch. Ration. Mech. Anal. , vol.94 , pp. 193-208
    • Levine, H.A.1    Weinberger, H.F.2
  • 127
    • 43049099339 scopus 로고    scopus 로고
    • The pseudoperturbation method in generalized eigenvalue problems
    • Loginov B.V., and Makeeva O.V. The pseudoperturbation method in generalized eigenvalue problems. Dokl. Math. 77 (2008) 194-197
    • (2008) Dokl. Math. , vol.77 , pp. 194-197
    • Loginov, B.V.1    Makeeva, O.V.2
  • 129
    • 7444237541 scopus 로고
    • Certain classes of extensions of a lacunary Hermitian operator
    • Malamud M.M. Certain classes of extensions of a lacunary Hermitian operator. Ukrainian Math. J. 44 2 (1992) 190-204
    • (1992) Ukrainian Math. J. , vol.44 , Issue.2 , pp. 190-204
    • Malamud, M.M.1
  • 130
    • 73749083057 scopus 로고
    • PhD thesis, Leningrad State University
    • V.G. Maz'ja, PhD thesis, Leningrad State University, 1965
    • (1965)
    • Maz'ja, V.G.1
  • 132
    • 84956116489 scopus 로고
    • Use of (p, l)-capacity in problems of the theory of exceptional sets
    • Maz'ja V.G., and Havin V.P. Use of (p, l)-capacity in problems of the theory of exceptional sets. Math. USSR Sbornik 19 4 (1973) 547-580
    • (1973) Math. USSR Sbornik , vol.19 , Issue.4 , pp. 547-580
    • Maz'ja, V.G.1    Havin, V.P.2
  • 133
    • 73749084282 scopus 로고    scopus 로고
    • The Dirichlet problem in Lipschitz domains with boundary data in Besov spaces for higher order elliptic systems with rough coefficients
    • in press
    • V. Maz'ya, M. Mitrea, T. Shaposhnikova, The Dirichlet problem in Lipschitz domains with boundary data in Besov spaces for higher order elliptic systems with rough coefficients, J. Analyse Math., in press
    • J. Analyse Math
    • Maz'ya, V.1    Mitrea, M.2    Shaposhnikova, T.3
  • 134
    • 0010347065 scopus 로고
    • Theory of Multipliers in Spaces of Differentiable Functions
    • Pitman (Advanced Publishing Program), Boston, MA
    • Maz'ya V.G., and Shaposhnikova T.O. Theory of Multipliers in Spaces of Differentiable Functions. Monogr. Stud. Math. vol. 23 (1985), Pitman (Advanced Publishing Program), Boston, MA
    • (1985) Monogr. Stud. Math. , vol.23
    • Maz'ya, V.G.1    Shaposhnikova, T.O.2
  • 135
    • 17244362427 scopus 로고    scopus 로고
    • Higher regularity in the layer potential theory for Lipschitz domains
    • Maz'ya V.G., and Shaposhnikova T.O. Higher regularity in the layer potential theory for Lipschitz domains. Indiana Univ. Math. J. 54 1 (2005) 99-142
    • (2005) Indiana Univ. Math. J. , vol.54 , Issue.1 , pp. 99-142
    • Maz'ya, V.G.1    Shaposhnikova, T.O.2
  • 137
    • 84975690753 scopus 로고
    • Distribution of the eigenvalues of finite multiplicity of Neumann extensions of an elliptic operator
    • (Russian); Engl. transl.:
    • Mikhaǐlets V.A. Distribution of the eigenvalues of finite multiplicity of Neumann extensions of an elliptic operator. Differ. Uravn. 30 (1994) 178-179 (Russian); Engl. transl.:
    • (1994) Differ. Uravn. , vol.30 , pp. 178-179
    • Mikhaǐlets, V.A.1
  • 138
    • 73749088013 scopus 로고
    • Distribution of the eigenvalues of finite multiplicity of Neumann extensions of an elliptic operator
    • Mikhaǐlets V.A. Distribution of the eigenvalues of finite multiplicity of Neumann extensions of an elliptic operator. Differ. Equ. 30 (1994) 167-168
    • (1994) Differ. Equ. , vol.30 , pp. 167-168
    • Mikhaǐlets, V.A.1
  • 139
    • 0001929311 scopus 로고    scopus 로고
    • Potential theory on Lipschitz domains in Riemannian manifolds: Sobolev-Besov space results and the Poisson problem
    • Mitrea M., and Taylor M. Potential theory on Lipschitz domains in Riemannian manifolds: Sobolev-Besov space results and the Poisson problem. J. Funct. Anal. 176 (2000) 1-79
    • (2000) J. Funct. Anal. , vol.176 , pp. 1-79
    • Mitrea, M.1    Taylor, M.2
  • 140
    • 27944471909 scopus 로고    scopus 로고
    • Lipschitz domains, domains with corners, and the Hodge Laplacian
    • Mitrea M., Taylor M., and Vasy A. Lipschitz domains, domains with corners, and the Hodge Laplacian. Comm. Partial Differential Equations 30 (2005) 1445-1462
    • (2005) Comm. Partial Differential Equations , vol.30 , pp. 1445-1462
    • Mitrea, M.1    Taylor, M.2    Vasy, A.3
  • 141
    • 0003360039 scopus 로고
    • Spherical Harmonics
    • Springer, Berlin
    • Müller K. Spherical Harmonics. Lecture Notes in Math. vol. 17 (1966), Springer, Berlin
    • (1966) Lecture Notes in Math. , vol.17
    • Müller, K.1
  • 142
    • 73749086003 scopus 로고
    • Applications of the Kreǐn resolvent formula to the theory of self-adjoint extensions of positive symmetric operators
    • Nenciu G. Applications of the Kreǐn resolvent formula to the theory of self-adjoint extensions of positive symmetric operators. J. Operator Theory 10 (1983) 209-218
    • (1983) J. Operator Theory , vol.10 , pp. 209-218
    • Nenciu, G.1
  • 143
    • 11944252724 scopus 로고    scopus 로고
    • Weyl asymptotic formula for the Laplacian on domains with rough boundaries
    • Netrusov Yu., and Safarov Yu. Weyl asymptotic formula for the Laplacian on domains with rough boundaries. Comm. Math. Phys. 253 2 (2005) 481-509
    • (2005) Comm. Math. Phys. , vol.253 , Issue.2 , pp. 481-509
    • Netrusov, Yu.1    Safarov, Yu.2
  • 144
    • 0038971119 scopus 로고
    • Inequalities for eigenvalues of membranes and plates
    • Payne L.E. Inequalities for eigenvalues of membranes and plates. J. Ration. Mech. Anal. 4 (1955) 517-529
    • (1955) J. Ration. Mech. Anal. , vol.4 , pp. 517-529
    • Payne, L.E.1
  • 145
    • 1642548420 scopus 로고
    • A note on inequalities for plate eigenvalues
    • Payne L.E. A note on inequalities for plate eigenvalues. J. Math. Phys. 39 (1960) 155-159
    • (1960) J. Math. Phys. , vol.39 , pp. 155-159
    • Payne, L.E.1
  • 146
    • 0000694219 scopus 로고
    • Isoperimetric inequalities and their applications
    • Payne L.E. Isoperimetric inequalities and their applications. SIAM Rev. 9 (1967) 453-488
    • (1967) SIAM Rev. , vol.9 , pp. 453-488
    • Payne, L.E.1
  • 147
    • 0141802608 scopus 로고
    • Some comments on the past fifty years of isoperimetric inequalities
    • Everitt W.N. (Ed), M. Dekker, New York
    • Payne L.E. Some comments on the past fifty years of isoperimetric inequalities. In: Everitt W.N. (Ed). Inequalities. Fifty Years on from Hardy, Littlewood and Pólya (1991), M. Dekker, New York 143-161
    • (1991) Inequalities. Fifty Years on from Hardy, Littlewood and Pólya , pp. 143-161
    • Payne, L.E.1
  • 148
    • 0000698220 scopus 로고
    • On the eigenvalue problem T u - λ S u = 0 with unbounded and nonsymmetric operators T and S
    • Petryshyn W.V. On the eigenvalue problem T u - λ S u = 0 with unbounded and nonsymmetric operators T and S. Philos. Trans. R. Soc. Lond. Ser. A 262 (1968) 413-458
    • (1968) Philos. Trans. R. Soc. Lond. Ser. A , vol.262 , pp. 413-458
    • Petryshyn, W.V.1
  • 149
    • 0002693554 scopus 로고
    • Dilation invariant estimates and the boundary Gårding inequality for higher order elliptic operators
    • Pipher J., and Verchota G.C. Dilation invariant estimates and the boundary Gårding inequality for higher order elliptic operators. Ann. Math. 142 (1995) 1-38
    • (1995) Ann. Math. , vol.142 , pp. 1-38
    • Pipher, J.1    Verchota, G.C.2
  • 150
    • 64549086918 scopus 로고    scopus 로고
    • Self-adjoint extensions of restrictions
    • Posilicano A. Self-adjoint extensions of restrictions. Oper. Matrices 2 (2008) 483-506
    • (2008) Oper. Matrices , vol.2 , pp. 483-506
    • Posilicano, A.1
  • 151
    • 64549139635 scopus 로고    scopus 로고
    • Krein's resolvent formula for self-adjoint extensions of symmetric second-order elliptic differential operators
    • 015204, 11 pp
    • Posilicano A., and Raimondi L. Krein's resolvent formula for self-adjoint extensions of symmetric second-order elliptic differential operators. J. Phys. A 42 (2009) 015204, 11 pp
    • (2009) J. Phys. A , vol.42
    • Posilicano, A.1    Raimondi, L.2
  • 152
    • 0013300671 scopus 로고    scopus 로고
    • On extremal positive operator extensions
    • Prokaj V., and Sebestyén Z. On extremal positive operator extensions. Acta Sci. Math. (Szeged) 62 (1996) 485-491
    • (1996) Acta Sci. Math. (Szeged) , vol.62 , pp. 485-491
    • Prokaj, V.1    Sebestyén, Z.2
  • 154
    • 73649211074 scopus 로고    scopus 로고
    • Criteria for Bochner's extension problem
    • preprint, arXiv:0802.0565v1
    • M. Ruzhansky, M. Sugimoto, Criteria for Bochner's extension problem, preprint, arXiv:0802.0565v1, 2008
    • (2008)
    • Ruzhansky, M.1    Sugimoto, M.2
  • 155
    • 0040036758 scopus 로고    scopus 로고
    • On restrictions and extensions of the Besov and Triebel-Lizorkin spaces with respect to Lipschitz domains
    • Rychkov V.S. On restrictions and extensions of the Besov and Triebel-Lizorkin spaces with respect to Lipschitz domains. J. London Math. Soc. (2) 60 (1999) 237-257
    • (1999) J. London Math. Soc. (2) , vol.60 , pp. 237-257
    • Rychkov, V.S.1
  • 156
    • 44649178596 scopus 로고    scopus 로고
    • A general boundary value problem and its Weyl function
    • Ryzhov V. A general boundary value problem and its Weyl function. Opuscula Math. 27 (2007) 305-331
    • (2007) Opuscula Math. , vol.27 , pp. 305-331
    • Ryzhov, V.1
  • 157
    • 61549085915 scopus 로고    scopus 로고
    • Weyl-Titchmarsh function of an abstract boundary value problem, operator colligations, and linear systems with boundary control
    • Ryzhov V. Weyl-Titchmarsh function of an abstract boundary value problem, operator colligations, and linear systems with boundary control. Complex Anal. Oper. Theory 3 (2009) 289-322
    • (2009) Complex Anal. Oper. Theory , vol.3 , pp. 289-322
    • Ryzhov, V.1
  • 158
    • 73749083451 scopus 로고    scopus 로고
    • Spectral boundary value problems and their linear operators
    • preprint, arXiv:0904.0276
    • V. Ryzhov, Spectral boundary value problems and their linear operators, preprint, arXiv:0904.0276, 2009
    • (2009)
    • Ryzhov, V.1
  • 159
    • 0003288250 scopus 로고    scopus 로고
    • The Asymptotic Distribution of Eigenvalues of Partial Differential Operators
    • Amer. Math. Soc., Providence, RI
    • Safarov Yu., and Vassiliev D. The Asymptotic Distribution of Eigenvalues of Partial Differential Operators. Transl. Math. Monogr. vol. 155 (1997), Amer. Math. Soc., Providence, RI
    • (1997) Transl. Math. Monogr. , vol.155
    • Safarov, Yu.1    Vassiliev, D.2
  • 160
    • 33645007303 scopus 로고    scopus 로고
    • On Krein-von Neumann and Friedrichs extensions
    • Sebestyén Z., and Sikolya E. On Krein-von Neumann and Friedrichs extensions. Acta Sci. Math. (Szeged) 69 (2003) 323-336
    • (2003) Acta Sci. Math. (Szeged) , vol.69 , pp. 323-336
    • Sebestyén, Z.1    Sikolya, E.2
  • 161
    • 0002672593 scopus 로고    scopus 로고
    • The classical moment problem as a self-adjoint finite difference operator
    • Simon B. The classical moment problem as a self-adjoint finite difference operator. Adv. Math. 137 (1998) 82-203
    • (1998) Adv. Math. , vol.137 , pp. 82-203
    • Simon, B.1
  • 162
    • 0040913724 scopus 로고
    • Positive self-adjoint extensions of operators affiliated with a von Neumann algebra
    • Skau C.F. Positive self-adjoint extensions of operators affiliated with a von Neumann algebra. Math. Scand. 44 (1979) 171-195
    • (1979) Math. Scand. , vol.44 , pp. 171-195
    • Skau, C.F.1
  • 163
    • 84975733045 scopus 로고
    • Convergence of Schrödinger operators on varying domains
    • Partial Differential Operators and Mathematical Physics. Demuth M., and Schulze B.-W. (Eds), Birkhäuser, Basel
    • Stollmann P. Convergence of Schrödinger operators on varying domains. In: Demuth M., and Schulze B.-W. (Eds). Partial Differential Operators and Mathematical Physics. Oper. Theory Adv. Appl. vol. 78 (1995), Birkhäuser, Basel 369-374
    • (1995) Oper. Theory Adv. Appl. , vol.78 , pp. 369-374
    • Stollmann, P.1
  • 164
    • 53349174196 scopus 로고    scopus 로고
    • On the hard and soft extensions of a nonnegative operator
    • Storozh O.G. On the hard and soft extensions of a nonnegative operator. J. Math. Sci. 79 (1996) 1378-1380
    • (1996) J. Math. Sci. , vol.79 , pp. 1378-1380
    • Storozh, O.G.1
  • 165
    • 73749085460 scopus 로고
    • On extensions of a semibounded operator
    • Štraus A.V. On extensions of a semibounded operator. Sovrem. Math. Dokl. 14 (1973) 1075-1079
    • (1973) Sovrem. Math. Dokl. , vol.14 , pp. 1075-1079
    • Štraus, A.V.1
  • 166
    • 0343766382 scopus 로고
    • The Cauchy Problem for Solutions of Elliptic Equations
    • Akademie Verlag, Berlin
    • Tarkhanov N.N. The Cauchy Problem for Solutions of Elliptic Equations. Math. Top. vol. 7 (1995), Akademie Verlag, Berlin
    • (1995) Math. Top. , vol.7
    • Tarkhanov, N.N.1
  • 167
    • 0034366511 scopus 로고    scopus 로고
    • Linear operator pencils A - λ B with discrete spectrum
    • Tretter C. Linear operator pencils A - λ B with discrete spectrum. Integral Equations Operator Theory 37 (2000) 357-373
    • (2000) Integral Equations Operator Theory , vol.37 , pp. 357-373
    • Tretter, C.1
  • 168
    • 0042420166 scopus 로고    scopus 로고
    • Function spaces in Lipschitz domains and on Lipschitz manifolds. Characteristic functions as pointwise multipliers
    • Triebel H. Function spaces in Lipschitz domains and on Lipschitz manifolds. Characteristic functions as pointwise multipliers. Rev. Mat. Complut. 15 (2002) 475-524
    • (2002) Rev. Mat. Complut. , vol.15 , pp. 475-524
    • Triebel, H.1
  • 170
    • 0039946629 scopus 로고
    • Non-self-adjoint accretive extensions of positive operators and theorems of Friedrichs-Krein-Phillips
    • Tsekanovskii E.R. Non-self-adjoint accretive extensions of positive operators and theorems of Friedrichs-Krein-Phillips. Funct. Anal. Appl. 14 (1980) 156-157
    • (1980) Funct. Anal. Appl. , vol.14 , pp. 156-157
    • Tsekanovskii, E.R.1
  • 171
    • 0039946633 scopus 로고
    • Friedrichs and Krein extensions of positive operators and holomorphic contraction semigroups
    • Tsekanovskii E.R. Friedrichs and Krein extensions of positive operators and holomorphic contraction semigroups. Funct. Anal. Appl. 15 (1981) 308-309
    • (1981) Funct. Anal. Appl. , vol.15 , pp. 308-309
    • Tsekanovskii, E.R.1
  • 172
    • 53149111361 scopus 로고
    • Characteristic function and sectorial boundary value problems
    • Issled. Geom. Mat. Anal. (in Russian)
    • Tsekanovskii E.R. Characteristic function and sectorial boundary value problems. Tr. Inst. Mat. (Novosibirsk) 200 7 (1987) 180-194 Issled. Geom. Mat. Anal. (in Russian)
    • (1987) Tr. Inst. Mat. (Novosibirsk) , vol.200 , Issue.7 , pp. 180-194
    • Tsekanovskii, E.R.1
  • 173
    • 0040539513 scopus 로고
    • Accretive extensions and problems on the Stieltjes operator-valued functions realizations
    • Operator Theory and Complex Analysis. Andom T., and Gohbergm I. (Eds), Birkhäuser, Basel
    • Tsekanovskii E.R. Accretive extensions and problems on the Stieltjes operator-valued functions realizations. In: Andom T., and Gohbergm I. (Eds). Operator Theory and Complex Analysis. Oper. Theory Adv. Appl. vol. 59 (1992), Birkhäuser, Basel 328-347
    • (1992) Oper. Theory Adv. Appl. , vol.59 , pp. 328-347
    • Tsekanovskii, E.R.1
  • 174
    • 0011038499 scopus 로고
    • On general boundary problems for elliptic differential equations
    • (Russian); Engl. transl.:
    • Višik M.L. On general boundary problems for elliptic differential equations. Tr. Mosk. Mat. Obs. 1 (1952) 187-246 (Russian); Engl. transl.:
    • (1952) Tr. Mosk. Mat. Obs. , vol.1 , pp. 187-246
    • Višik, M.L.1
  • 175
    • 0000731889 scopus 로고
    • On general boundary problems for elliptic differential equations
    • Višik M.L. On general boundary problems for elliptic differential equations. Amer. Math. Soc. Transl. Ser. 2 24 (1963) 107-172
    • (1963) Amer. Math. Soc. Transl. Ser. 2 , vol.24 , pp. 107-172
    • Višik, M.L.1
  • 176
    • 2942734295 scopus 로고
    • Allgemeine Eigenwerttheorie Hermitescher Funktionaloperatoren
    • von Neumann J. Allgemeine Eigenwerttheorie Hermitescher Funktionaloperatoren. Math. Ann. 102 (1929/1930) 49-131
    • (1929) Math. Ann. , vol.102 , pp. 49-131
    • von Neumann, J.1
  • 178
    • 0003276928 scopus 로고
    • Linear Operators in Hilbert Spaces
    • Springer, New York
    • Weidmann J. Linear Operators in Hilbert Spaces. Grad. Texts in Math. vol. 68 (1980), Springer, New York
    • (1980) Grad. Texts in Math. , vol.68
    • Weidmann, J.1
  • 179
    • 0002182320 scopus 로고
    • Stetige Abhängigkeit der Eigenwerte und Eigenfunktionen elliptischer Differentialoperatoren vom Gebiet
    • Weidmann J. Stetige Abhängigkeit der Eigenwerte und Eigenfunktionen elliptischer Differentialoperatoren vom Gebiet. Math. Scand. 54 (1984) 51-69
    • (1984) Math. Scand. , vol.54 , pp. 51-69
    • Weidmann, J.1
  • 181
    • 0039180579 scopus 로고
    • Über die Abhängigkeit der Eigenschwingungen einer Membran und deren Begrenzung
    • Weyl H. Über die Abhängigkeit der Eigenschwingungen einer Membran und deren Begrenzung. J. Reine Angew. Math. 141 (1912) 1-11
    • (1912) J. Reine Angew. Math. , vol.141 , pp. 1-11
    • Weyl, H.1
  • 182
    • 0001117305 scopus 로고
    • Das asymptotische Verteilungsgesetz der Eigenwerte linearer partieller Diferentialgleichungen (mit einer Anwendung auf die Theorie der Hohlraumstrahlung)
    • Weyl H. Das asymptotische Verteilungsgesetz der Eigenwerte linearer partieller Diferentialgleichungen (mit einer Anwendung auf die Theorie der Hohlraumstrahlung). Math. Ann. 71 (1912) 441-479
    • (1912) Math. Ann. , vol.71 , pp. 441-479
    • Weyl, H.1
  • 183
    • 53249149321 scopus 로고
    • Ramifications, old and new, of the eigenvalue problem
    • Weyl H. Ramifications, old and new, of the eigenvalue problem. Bull. Amer. Math. Soc. (N.S.) 56 (1950) 115-139
    • (1950) Bull. Amer. Math. Soc. (N.S.) , vol.56 , pp. 115-139
    • Weyl, H.1
  • 184
    • 0003320023 scopus 로고
    • Weakly Differentiable Functions
    • Springer, New York
    • Ziemer W.P. Weakly Differentiable Functions. Grad. Texts in Math. vol. 120 (1989), Springer, New York
    • (1989) Grad. Texts in Math. , vol.120
    • Ziemer, W.P.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.