메뉴 건너뛰기




Volumn 36, Issue 9, 2011, Pages 1521-1543

On riesz means of eigenvalues

Author keywords

Berezin li yau inequalities; Eigenvalues; Laplacian; Universal bounds

Indexed keywords


EID: 80051683101     PISSN: 03605302     EISSN: 15324133     Source Type: Journal    
DOI: 10.1080/03605302.2011.595865     Document Type: Article
Times cited : (16)

References (56)
  • 2
    • 0000545486 scopus 로고
    • On semi-classical bounds for eigenvalues of Schröinger operators
    • Aizenman, M., Lieb, E.H. (1978). On semi-classical bounds for eigenvalues of Schröinger operators. Phys. Lett. 66A:427-429.
    • (1978) Phys. Lett , vol.66 A , pp. 427-429
    • Aizenman, M.1    Lieb, E.H.2
  • 3
    • 0011448796 scopus 로고
    • Lower bounds on the number of points in the lower spectrum of elliptic operators
    • Allegretto, W. (1979). Lower bounds on the number of points in the lower spectrum of elliptic operators. Can. J. Math. 31:419-426.
    • (1979) Can. J. Math , vol.31 , pp. 419-426
    • Allegretto, W.1
  • 4
    • 0036475162 scopus 로고    scopus 로고
    • The universal eigenvalue bounds of Payne-Póya- Weinberger
    • Hile-Protter, and H. C. Yang, Proc. Indian Acad. Sci. Math. Sci
    • Ashbaugh, M.S. (2002). The universal eigenvalue bounds of Payne-Póya- Weinberger, Hile-Protter, and H. C. Yang. Proc. Indian Acad. Sci. Math. Sci. 112:3-30.
    • (2002) , vol.112 , pp. 3-30
    • Ashbaugh, M.S.1
  • 6
    • 12744260598 scopus 로고    scopus 로고
    • A unified approach to universal inequalities for eigenvalues of elliptic operators
    • Ashbaugh, M.S., Hermi, L. (2004). A unified approach to universal inequalities for eigenvalues of elliptic operators. Pacific J. Math. 217:201-220.
    • (2004) Pacific J. Math , vol.217 , pp. 201-220
    • Ashbaugh, M.S.1    Hermi, L.2
  • 9
    • 0001146196 scopus 로고
    • Convariant and contravariant symbols of operators
    • in Russian); English translation in Math. USSRIzv.6:1117-1151
    • Berezin, F. (1972). Convariant and contravariant symbols of operators. Izv. Akad. Nauk SSSR 37:1134-1167 (in Russian); English translation in Math. USSRIzv.6:1117-1151.
    • (1972) Izv. Akad. Nauk SSSR , vol.37 , pp. 1134-1167
    • Berezin, F.1
  • 12
    • 33751116288 scopus 로고    scopus 로고
    • Bounds on eigenvalues of Dirichlet Laplacian
    • Cheng, Q.M., Yang, H.C. (2007). Bounds on eigenvalues of Dirichlet Laplacian. Math. Ann. 337:159-175.
    • (2007) Math. Ann , vol.337 , pp. 159-175
    • Cheng, Q.M.1    Yang, H.C.2
  • 13
    • 0038858936 scopus 로고
    • An isoperimetric inequality for the eigenfunctions of linear second order elliptic operators
    • Chiti, G. (1982). An isoperimetric inequality for the eigenfunctions of linear second order elliptic operators. Boll. Un. Mat. Ital. (6) 1-A:145-151.
    • (1982) Boll. Un. Mat. Ital , vol.6 , Issue.1 A , pp. 145-151
    • Chiti, G.1
  • 14
    • 0003287060 scopus 로고
    • Heat Kernels and Spectral Theory
    • Cambridge: Cambridge University Press
    • Davies, E.B. (1989). Heat Kernels and Spectral Theory. Cambridge Tracts in Mathematics, Vol. 92. Cambridge: Cambridge University Press.
    • (1989) Cambridge Tracts in Mathematics , vol.92
    • Davies, E.B.1
  • 15
    • 0003288852 scopus 로고
    • Spectral Theory and Differential Operators
    • Cambridge: Cambridge University Press
    • Davies, E.B. (1995). Spectral Theory and Differential Operators. Cambridge Studies in Advanced Mathematics, Vol. 42. Cambridge: Cambridge University Press.
    • (1995) Cambridge Studies in Advanced Mathematics , vol.42
    • Davies, E.B.1
  • 16
    • 33746335683 scopus 로고    scopus 로고
    • Lieb-Thirring type inequalities and Gagliardo-Nirenberg inequalities for systems
    • Dolbeault, J., Felmer, P., Loss, M., Paturel, E. (2006). Lieb-Thirring type inequalities and Gagliardo-Nirenberg inequalities for systems. J. Funct. Anal. 238:193-220.
    • (2006) J. Funct. Anal , vol.238 , pp. 193-220
    • Dolbeault, J.1    Felmer, P.2    Loss, M.3    Paturel, E.4
  • 17
    • 50849102620 scopus 로고    scopus 로고
    • Compactness properties for trace-class operators and applications to quantum mechanics
    • Dolbeault, J., Felmer, P., Mayorga-Zambrano, J. (2008). Compactness properties for trace-class operators and applications to quantum mechanics. Monatsh. Math. 155:43-66.
    • (2008) Monatsh. Math , vol.155 , pp. 43-66
    • Dolbeault, J.1    Felmer, P.2    Mayorga-Zambrano, J.3
  • 18
    • 68949106024 scopus 로고    scopus 로고
    • Universal inequalities for the eigenvalues of Laplace and Schröinger operators on submanifolds
    • El Soufi, A., Harrell, E.M., Ilias, S. (2009). Universal inequalities for the eigenvalues of Laplace and Schröinger operators on submanifolds. Trans. Amer. Math. Soc. 361:2237-2350.
    • (2009) Trans. Amer. Math. Soc , vol.361 , pp. 2237-2350
    • el Soufi, A.1    Harrell, E.M.2    Ilias, S.3
  • 20
    • 80051684165 scopus 로고    scopus 로고
    • Remarks on eigenvalue estimates and semigroup domination
    • Frank, R. (2009). Remarks on eigenvalue estimates and semigroup domination. Preprint 2009.
    • (2009) Preprint 2009
    • Frank, R.1
  • 21
    • 77950621483 scopus 로고    scopus 로고
    • Some eigenvalue inequalities for Schröinger operators with positive potentials
    • Frank, R., Laptev, A., Molchanov, S. (2008). Some eigenvalue inequalities for Schröinger operators with positive potentials. Proc. Amer. Math. Soc. 136:4245-4255.
    • (2008) Proc. Amer. Math. Soc , vol.136 , pp. 4245-4255
    • Frank, R.1    Laptev, A.2    Molchanov, S.3
  • 22
    • 74349087923 scopus 로고    scopus 로고
    • Póya's conjecture in the presence of a constant magnetic field
    • Frank, R., Laptev, A., Weidl, T. (2009). Póya's conjecture in the presence of a constant magnetic field. J. Eur. Math. Soc. 11:1365-1383.
    • (2009) J. Eur. Math. Soc , vol.11 , pp. 1365-1383
    • Frank, R.1    Laptev, A.2    Weidl, T.3
  • 24
    • 33947172418 scopus 로고    scopus 로고
    • Commutators, eigenvalue gaps, and mean curvature in the theory of Schröinger operators
    • Harrell, E.M. (2007). Commutators, eigenvalue gaps, and mean curvature in the theory of Schröinger operators. Comm. Part. Diff. Eqs. 32:401-413.
    • (2007) Comm. Part. Diff. Eqs , vol.32 , pp. 401-413
    • Harrell, E.M.1
  • 25
    • 43049110988 scopus 로고    scopus 로고
    • Differential inequalities for Riesz means and Weyl-type bounds for eigenvalues
    • Harrell, E.M., Hermi, L. (2008). Differential inequalities for Riesz means and Weyl-type bounds for eigenvalues. J. Funct. Anal. 254:3173-3191.
    • (2008) J. Funct. Anal , vol.254 , pp. 3173-3191
    • Harrell, E.M.1    Hermi, L.2
  • 26
    • 21744444664 scopus 로고    scopus 로고
    • On trace identities and universal eigenvalue estimates for some partial differential operators
    • Harrell, E.M., Stubbe, J. (1997). On trace identities and universal eigenvalue estimates for some partial differential operators. Trans. Amer. Math. Soc.349:1797-1809.
    • (1997) Trans. Amer. Math. Soc , vol.349 , pp. 1797-1809
    • Harrell, E.M.1    Stubbe, J.2
  • 27
    • 80051702931 scopus 로고    scopus 로고
    • Trace identities for commutators, with applications to the distribution of eigenvalues
    • Harrell, E.M., Stubbe, J. Trace identities for commutators, with applications to the distribution of eigenvalues. To appear in Trans. Amer. Math. Soc.
    • To Appear In Trans. Amer. Math. Soc
    • Harrell, E.M.1    Stubbe, J.2
  • 28
    • 84974766437 scopus 로고
    • Riesz means of bound states and semiclassical limit connected with a Lieb-Thirring's conjecture
    • Helffer, B., Robert, D. (1990). Riesz means of bound states and semiclassical limit connected with a Lieb-Thirring's conjecture. Asymptotic Anal. 3:91-103.
    • (1990) Asymptotic Anal , vol.3 , pp. 91-103
    • Helffer, B.1    Robert, D.2
  • 29
    • 0000840123 scopus 로고
    • Riesz means of bounded states and semi-classical limit connected with a Lieb-Thirring conjecture, II
    • Helffer, B., Robert, D. (1990). Riesz means of bounded states and semi-classical limit connected with a Lieb-Thirring conjecture, II. Ann. Inst. H. Poincaré Phys. Théor. 53:139-147.
    • (1990) Ann. Inst. H. Poincaré Phys. Théor , vol.53 , pp. 139-147
    • Helffer, B.1    Robert, D.2
  • 30
    • 43049116937 scopus 로고    scopus 로고
    • Two new Weyl-type bounds for the Dirichlet Laplacian
    • Hermi, L. (2008). Two new Weyl-type bounds for the Dirichlet Laplacian. Trans. Amer. Math. Soc. 360:1539-1558.
    • (2008) Trans. Amer. Math. Soc , vol.360 , pp. 1539-1558
    • Hermi, L.1
  • 31
    • 0000582072 scopus 로고
    • Inequalities for eigenvalues of the Laplacian
    • Hile, G.N., Protter, M.H. (1980). Inequalities for eigenvalues of the Laplacian. Indiana Univ. Math. J. 29:523-538.
    • (1980) Indiana Univ Math. J , vol.29 , pp. 523-538
    • Hile, G.N.1    Protter, M.H.2
  • 32
    • 0036552286 scopus 로고    scopus 로고
    • On the number of bound states for Schringer operators with operator-valued potentials
    • Hundertmark, D. (2002). On the number of bound states for Schringer operators with operator-valued potentials. Arkiv för Matematik 40:73-87.
    • (2002) Arkiv För Matematik , vol.40 , pp. 73-87
    • Hundertmark, D.1
  • 33
    • 46749084507 scopus 로고    scopus 로고
    • Some bound state problems in Quantum Mechanics
    • In: Gesztesy, F., ed., Proceedings of Symposia in PureMathematics, Part 1. Providence, RI: American Mathematical Society
    • Hundertmark, D. (2007). Some bound state problems in Quantum Mechanics. In: Gesztesy, F., ed. Spectral Theory and Mathematical Physics: A Festschrift in Honor of Barry Simon's 60th Birthday. Proceedings of Symposia in PureMathematics, Vol. 76, Part 1. Providence, RI: American Mathematical Society, pp. 463-496.
    • (2007) Spectral Theory and Mathematical Physics: A Festschrift In Honor of Barry Simon's 60th Birthday , vol.76 , pp. 463-496
    • Hundertmark, D.1
  • 34
    • 0342876907 scopus 로고
    • Quantum mechanical sum rules
    • Jackiw, R. (1967). Quantum mechanical sum rules. Phys. Rev. 157:1220-1225.
    • (1967) Phys. Rev , vol.157 , pp. 1220-1225
    • Jackiw, R.1
  • 35
    • 0003021436 scopus 로고
    • In: Neyman, J., ed. Proceedings of the Second erkeley Symposium on Mathematical Statistics and Probability, Berkeley and Los Angeles: University of California Press
    • Kac, M. (1951). On some connections between probability theory and differential and integral equations. In: Neyman, J., ed. Proceedings of the Second erkeley Symposium on Mathematical Statistics and Probability, 1950. Berkeley and Los Angeles: University of California Press, pp. 189-215.
    • (1951) On Some Connections Between Probability Theory and Differential and Integral Equations , pp. 189-215
    • Kac, M.1
  • 36
    • 0002697827 scopus 로고
    • Can one hear the shape of a drum?
    • Kac, M. (1966). Can one hear the shape of a drum? Amer. Math. Monthly 73:1-23.
    • (1966) Amer. Math. Monthly , vol.73 , pp. 1-23
    • Kac, M.1
  • 37
    • 0003346969 scopus 로고
    • Perturbation Theory For Linear Operators
    • New York: Springer-Verlag
    • Kato, T. (1966). Perturbation Theory for Linear Operators. Grundlehren der Mathematischen Wissenchaften. Vol. 132. New York: Springer-Verlag.
    • (1966) Grundlehren der Mathematischen Wissenchaften , vol.132
    • Kato, T.1
  • 38
    • 38249011890 scopus 로고
    • Upper bounds for the Neumann eigenvalues on a bounded domain in Euclidean space
    • Kréer, P. (1992). Upper bounds for the Neumann eigenvalues on a bounded domain in Euclidean space. J. Funct. Anal. 106:353-357.
    • (1992) J. Funct. Anal , vol.106 , pp. 353-357
    • Kréer, P.1
  • 39
    • 0031574602 scopus 로고    scopus 로고
    • Dirichlet and Neumann eigenvalue problems on domains in Euclidean spaces
    • Laptev, A. (1997). Dirichlet and Neumann eigenvalue problems on domains in Euclidean spaces. J. Funct. Anal. 151:531-545.
    • (1997) J. Funct. Anal , vol.151 , pp. 531-545
    • Laptev, A.1
  • 40
    • 33746709985 scopus 로고    scopus 로고
    • On the Lieb-Thirring conjecture for a class of potentials
    • In: Rossmann, J., P., Wildenhain, G., eds., Rostock, 1998). Operator Theory and Advances and Applications, Vol. 110. Basel: Birkhser
    • Laptev, A. (1999). On the Lieb-Thirring conjecture for a class of potentials. In: Rossmann, J., P., Wildenhain, G., eds. The Maz'ya Anniversary Collection, Vol. 2 (Rostock, 1998). Operator Theory and Advances and Applications, Vol. 110. Basel: Birkhser, pp. 227-234.
    • (1999) The Maz'ya Anniversary Collection , vol.2 , pp. 227-234
    • Laptev, A.1
  • 41
    • 0002983823 scopus 로고    scopus 로고
    • Sharp Lieb-Thirring inequalities in high dimensions
    • Laptev, A., Weidl, T. (2000). Sharp Lieb-Thirring inequalities in high dimensions. Acta Math. 184:87-111.
    • (2000) Acta Math , vol.184 , pp. 87-111
    • Laptev, A.1    Weidl, T.2
  • 42
    • 77951695367 scopus 로고    scopus 로고
    • Recent results on Lieb-Thirring inequalities
    • (La Chapelle sur Erdre, 2000), Exp. No. 88. Nantes, France: University of Nantes
    • Laptev, A., Weidl, T. (2000). Recent results on Lieb-Thirring inequalities. Journées "Équations aux Dérivées Partielles" (La Chapelle sur Erdre, 2000), Exp. No. 88. Nantes, France: University of Nantes.
    • (2000) Journées "Équations Aux Dérivées Partielles"
    • Laptev, A.1    Weidl, T.2
  • 43
    • 0037055186 scopus 로고    scopus 로고
    • Commutators, spectral trace identities, and universal estimates for eigenvalues
    • Levitin, M., Parnovski, L. (2002). Commutators, spectral trace identities, and universal estimates for eigenvalues. J. Funct. Anal. 192:425-445.
    • (2002) J. Funct. Anal , vol.192 , pp. 425-445
    • Levitin, M.1    Parnovski, L.2
  • 44
    • 0000538029 scopus 로고
    • On the Schröinger equation and the eigenvalue problem
    • Li, P., Yau, S.-T. (1983). On the Schröinger equation and the eigenvalue problem. Comm. Math. Phys. 88:309-318.
    • (1983) Comm. Math. Phys , vol.88 , pp. 309-318
    • Li, P.1    Yau, S.-T.2
  • 45
    • 0037319507 scopus 로고    scopus 로고
    • A lower bound for sums of eigenvalues of the Laplacian
    • Melas, A.D. (2003). A lower bound for sums of eigenvalues of the Laplacian. Proc. Amer. Math. Soc. 131:631-636.
    • (2003) Proc. Amer. Math. Soc , vol.131 , pp. 631-636
    • Melas, A.D.1
  • 46
    • 84963097105 scopus 로고
    • On the eigenvalues of vibrating membranes
    • Póya, G. (1961). On the eigenvalues of vibrating membranes. Proc. London Math. Soc. 11:419-433.
    • (1961) Proc. London Math. Soc , vol.11 , pp. 419-433
    • Póya, G.1
  • 47
    • 0023364305 scopus 로고
    • Can one hear the shape of a drum? revisited
    • Protter, M.H. (1987). Can one hear the shape of a drum? revisited. SIAM Rev. 29:185-197.
    • (1987) SIAM Rev , vol.29 , pp. 185-197
    • Protter, M.H.1
  • 48
    • 84966242938 scopus 로고
    • On spectra of second-order differential operators
    • Ray, D. (1954). On spectra of second-order differential operators. Trans. Amer. Math. Soc. 77:299-321.
    • (1954) Trans. Amer. Math. Soc , vol.77 , pp. 299-321
    • Ray, D.1
  • 49
    • 0003352781 scopus 로고
    • Methods of Modern Mathematical Physics, II
    • New York: Academic Press
    • Reed, M., Simon, B. (1975). Methods of Modern Mathematical Physics, II. Fourier Analysis, Self-Adjointness. New York: Academic Press.
    • (1975) Fourier Analysis, Self-Adjointness
    • Reed, M.1    Simon, B.2
  • 51
    • 77950596716 scopus 로고    scopus 로고
    • Lower bounds for the generalized counting function
    • In: Rossmann, J., Takáč, P., Wildenhain, G., eds., Rostock, 1998). Operator Theory and Advances and Applications, Vol. 110. Basel: Birkhöser
    • Safarov, Y. (1999). Lower bounds for the generalized counting function. In: Rossmann, J., Takáč, P., Wildenhain, G., eds. The Maz'ya Anniversary Collection, Vol. 2 (Rostock, 1998). Operator Theory and Advances and Applications, Vol. 110. Basel: Birkhöser, pp. 275-293.
    • (1999) The Maz'ya Anniversary Collection , vol.2 , pp. 275-293
    • Safarov, Y.1
  • 52
    • 80051682132 scopus 로고    scopus 로고
    • Schröinger operators with purely discrete spectrum
    • Simon, B. (2009). Schröinger operators with purely discrete spectrum. Methods Funct. Anal. Topology 15:61-66.
    • (2009) Methods Funct. Anal. Topology , vol.15 , pp. 61-66
    • Simon, B.1
  • 53
    • 0011273813 scopus 로고
    • Bounds on Green's functions of second-order differential equations
    • Van den Berg, M. (1981). Bounds on Green's functions of second-order differential equations. J. Math. Phys. 22:2452-2455.
    • (1981) J. Math. Phys , vol.22 , pp. 2452-2455
    • van den Berg, M.1
  • 55
    • 80051697239 scopus 로고
    • Das asymptotische Verteilungsgesetz der Eigenwerte linearer partieller ifferentialgleichungen
    • Weyl, H. (1911). Das asymptotische Verteilungsgesetz der Eigenwerte linearer partieller ifferentialgleichungen [The asymptotic distribution law of the eigenvalues of linear partial differential equations]. Math. Ann. 71:441-479.
    • (1911) Math. Ann , vol.71 , pp. 441-479
    • Weyl, H.1
  • 56
    • 3142627946 scopus 로고
    • Revision of International Centre for Theoretical Physics preprint IC/91/60, Trieste, Italy, April 1991
    • Yang, H.C. (1995). Estimates of the difference between consecutive eigenvalues. (Revision of International Centre for Theoretical Physics preprint IC/91/60, Trieste, Italy, April 1991).
    • (1995) Estimates of the Difference Between Consecutive Eigenvalues
    • Yang, H.C.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.