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Volumn 87, Issue 1-2, 1980, Pages 1-34

Singular eigenvalue problems with eigenvalue parameter contained in the boundary conditions

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EID: 84971128441     PISSN: 03082105     EISSN: 14737124     Source Type: Journal    
DOI: 10.1017/S0308210500012312     Document Type: Article
Times cited : (91)

References (74)
  • 3
    • 84966262484 scopus 로고
    • (Reading, Mass.: Addison-Wesley
    • L. Breiman. Probability (Reading, Mass.: Addison-Wesley, 1968).
    • (1968) Probability
    • Breiman, L.1
  • 6
    • 33746854828 scopus 로고
    • Self-adjoint subspace extensions of non-densely defined symmetric operators
    • E. A. Coddington. Self-adjoint subspace extensions of non-densely defined symmetric operators. Advances in Math. 14 (1974), 309-332.
    • (1974) Advances in Math , vol.14 , pp. 309-332
    • Coddington, E.A.1
  • 7
    • 0010709088 scopus 로고
    • Self-adjoint problems for nondensely defined ordinary differential operators and their eigenfunction expansions
    • E. A. Coddington. Self-adjoint problems for nondensely defined ordinary differential operators and their eigenfunction expansions. Advances in Math. 15 (1975), 1-40.
    • (1975) Advances in Math , vol.15 , pp. 1-40
    • Coddington, E.A.1
  • 8
    • 0001298838 scopus 로고
    • Self-adjoint subspaces and eigenfunction expansions for ordinary differential subspaces
    • E. A. Coddington and A. Dijksma. Self-adjoint subspaces and eigenfunction expansions for ordinary differential subspaces. J. Differential Equations 20 (1976), 473-526.
    • (1976) J. Differential Equations , vol.20 , pp. 473-526
    • Coddington, E.A.1    Dijksma, A.2
  • 10
    • 49549144336 scopus 로고
    • Eigenfunction expansions for nondensely defined differential operators
    • A. Dijksma and H. S. V. de Snoo. Eigenfunction expansions for nondensely defined differential operators. J. Differential Equations 17 (1975), 198-219.
    • (1975) J. Differential Equations , vol.17 , pp. 198-219
    • Dijksma, A.1    de Snoo, H.S.V.2
  • 11
    • 0013481128 scopus 로고
    • Self-adjoint extensions of symmetric subspaces
    • A. Dijksma and H. S. V. de Snoo. Self-adjoint extensions of symmetric subspaces. Pacific J. Math. 54 (1974), 71-100.
    • (1974) Pacific J. Math , vol.54 , pp. 71-100
    • Dijksma, A.1    de Snoo, H.S.V.2
  • 12
    • 34250431227 scopus 로고
    • Integral transforms and a class of singular S-hermitian eigenvalue problems
    • A. Dijksma and H. S. V. de Snoo. Integral transforms and a class of singular S-hermitian eigenvalue problems. Manuscripta Math. 10 (1973), 129-139.
    • (1973) Manuscripta Math , vol.10 , pp. 129-139
    • Dijksma, A.1    de Snoo, H.S.V.2
  • 13
    • 77955340534 scopus 로고
    • An integral transform associated with boundary conditions containing an eigenvalue parameter
    • D. S. Cohen. An integral transform associated with boundary conditions containing an eigenvalue parameter. SIAM J. Appl. Math. 14 (1966), 1164-1175.
    • (1966) SIAM J. Appl. Math , vol.14 , pp. 1164-1175
    • Cohen, D.S.1
  • 16
    • 84959808377 scopus 로고
    • On a property of the m-coefficient of a second-order linear differential equation
    • W. N. Everitt. On a property of the m-coefficient of a second-order linear differential equation. J. London Math. Soc. 4 (1972), 443-457.
    • (1972) J. London Math. Soc , vol.4 , pp. 443-457
    • Everitt, W.N.1
  • 17
    • 0001254093 scopus 로고
    • The parabolic differential equations and the associated semigroups of transforms
    • W. Feller. The parabolic differential equations and the associated semigroups of transforms. Ann. of Math. 55 (1952), 468-519.
    • (1952) Ann. of Math , vol.55 , pp. 468-519
    • Feller, W.1
  • 18
    • 84972541408 scopus 로고
    • Generalized second-order differential operators and their lateral conditions
    • W. Feller. Generalized second-order differential operators and their lateral conditions. Illinois J. Math. 1 (1957), 459-504.
    • (1957) Illinois J. Math , vol.1 , pp. 459-504
    • Feller, W.1
  • 19
    • 84980081773 scopus 로고
    • On differential operators and boundary conditions
    • W. Feller. On differential operators and boundary conditions. Comm. Pure Appl. Math. 8 (1955), 203-216.
    • (1955) Comm. Pure Appl. Math , vol.8 , pp. 203-216
    • Feller, W.1
  • 20
    • 84966207705 scopus 로고
    • Diffusion processes in one dimension
    • W. Feller. Diffusion processes in one dimension. Trans. Amer. Math. Soc. 77 (1954), 1-31.
    • (1954) Trans. Amer. Math. Soc , vol.77 , pp. 1-31
    • Feller, W.1
  • 21
    • 0001277826 scopus 로고
    • Two singular diffusion problems
    • W. Feller. Two singular diffusion problems. Ann. of Math. 54 (1951), 173-182.
    • (1951) Ann. of Math , vol.54 , pp. 173-182
    • Feller, W.1
  • 24
    • 84968492701 scopus 로고
    • Parametrizations of Titchmarsh's m(A)-functions in the limit circle case
    • C. Fulton. Parametrizations of Titchmarsh's m(A)-functions in the limit circle case. Trans. Amer. Math. Soc. 229 (1977), 51-63.
    • (1977) Trans. Amer. Math. Soc , vol.229 , pp. 51-63
    • Fulton, C.1
  • 26
    • 84971166919 scopus 로고
    • Two-point boundary value problems with eigenvalue parameter contained in the boundary conditions
    • C. Fulton. Two-point boundary value problems with eigenvalue parameter contained in the boundary conditions. Proc. Roy. Soc. Edinburgh Sect. A 77 (1977), 293-308.
    • (1977) Proc. Roy. Soc. Edinburgh Sect. A , vol.77 , pp. 293-308
    • Fulton, C.1
  • 27
    • 0018530885 scopus 로고
    • Numerical methods for a singular eigenvalue problem with eigenparameter in the boundary conditions
    • C. Fulton and S. Pruess. Numerical methods for a singular eigenvalue problem with eigenparameter in the boundary conditions. J. Math. Anal. Appl. 71 (1979), 431-462.
    • (1979) J. Math. Anal. Appl , vol.71 , pp. 431-462
    • Fulton, C.1    Pruess, S.2
  • 29
    • 0000252989 scopus 로고
    • Differential equations with nonoscillatory eigenfunctions
    • P. Hartman. Differential equations with nonoscillatory eigenfunctions. Duke Math. J. 15 (1948), 697-709.
    • (1948) Duke Math. J , vol.15 , pp. 697-709
    • Hartman, P.1
  • 30
    • 84971123863 scopus 로고
    • G. Hellwig. Differential operators of mathematical physics (Engl. transl.) (Reading, Mass.: Addison-Wesley, 1967).
    • (1967)
    • Hellwig, G.1
  • 31
    • 34250966824 scopus 로고
    • Anfangs- und Randwertprobleme bei partiellen Differentialgleichungen von wechselndem Typus auf den Rändern
    • G. Hellwig. Anfangs- und Randwertprobleme bei partiellen Differentialgleichungen von wechselndem Typus auf den Rändern. Math. Z. 58 (1953), 337-357.
    • (1953) Math. Z , vol.58 , pp. 337-357
    • Hellwig, G.1
  • 32
    • 33947658275 scopus 로고
    • über die Anwendung der Laplace-transformation auf Randwert-probleme
    • G. Hellwig. über die Anwendung der Laplace-transformation auf Randwert-probleme. Math. Z. (1957), 371-388.
    • (1957) Math. Z , pp. 371-388
    • Hellwig, G.1
  • 33
    • 84979325785 scopus 로고
    • über die Anwendung der Laplace-transformation auf Ausgleichsprobleme
    • G. Hellwig. über die Anwendung der Laplace-transformation auf Ausgleichsprobleme. Math. Nachr. 18 (1958), 281-291.
    • (1958) Math. Nachr , vol.18 , pp. 281-291
    • Hellwig, G.1
  • 36
    • 0003127680 scopus 로고
    • R-Functions-Analytic functions mapping the upper halfplane into itself
    • (Engl. transl. of Supplement I of the Russian translation of reference [2], Moscow, 1968
    • I. S. Kac and M. G. Krein. R-Functions-Analytic functions mapping the upper halfplane into itself. Amer. Math. Soc. Transl. (2) 103 (1974), 1-18 (Engl. transl. of Supplement I of the Russian translation of reference [2], Moscow, 1968).
    • (1974) Amer. Math. Soc. Transl , vol.103 , Issue.2 , pp. 1-18
    • Kac, I.S.1    Krein, M.G.2
  • 37
    • 0000164605 scopus 로고
    • The eigenvalue problem for ordinary differential equations of the second order and Heisenberg's theory of S-matrices
    • K. Kodaira. The eigenvalue problem for ordinary differential equations of the second order and Heisenberg's theory of S-matrices. Amer. J. Math. 71 (1949), 921-945.
    • (1949) Amer. J. Math , vol.71 , pp. 921-945
    • Kodaira, K.1
  • 39
    • 0003299184 scopus 로고
    • A problem in diffusion or in the flow of heat for a solid in contact with a fluid
    • R. E. Langer. A problem in diffusion or in the flow of heat for a solid in contact with a fluid. Tôhoku Math. J. 35 (1932), 360-375.
    • (1932) Tôhoku Math. J , vol.35 , pp. 360-375
    • Langer, R.E.1
  • 40
    • 33745992681 scopus 로고
    • A simplified proof of the expansion theorem for singular second order linear differential equations
    • N. Levinson. A simplified proof of the expansion theorem for singular second order linear differential equations. Duke Math. J. 18 (1951), 57-71.
    • (1951) Duke Math. J , vol.18 , pp. 57-71
    • Levinson, N.1
  • 43
    • 0000572722 scopus 로고
    • On the asymptotic behaviour of the spectral function of a self-adjoint differential equation of the second order
    • B. M. Levitan. On the asymptotic behaviour of the spectral function of a self-adjoint differential equation of the second order. Izv. Akad. Nauk SSSR Ser. Mat. 16 (1952), 325-352;
    • (1952) Izv. Akad. Nauk SSSR Ser. Mat , vol.16 , pp. 325-352
    • Levitan, B.M.1
  • 45
    • 0040536382 scopus 로고
    • On the asymptotic behaviour of the spectral function of a self-adjoint differential equation of the second order and on eigenfunction expansions, II
    • B. M. Levitan. On the asymptotic behaviour of the spectral function of a self-adjoint differential equation of the second order and on eigenfunction expansions, II. Izv. Akad. Nauk SSSR Ser. Mat 19 (1955), 33-58;
    • (1955) Izv. Akad. Nauk SSSR Ser. Mat , vol.19 , pp. 33-58
    • Levitan, B.M.1
  • 47
    • 84965864584 scopus 로고
    • (2nd edn) (Princeton: Van Nostrand
    • M. Loeve. Probability theory (2nd edn) (Princeton: Van Nostrand, 1960).
    • (1960) Probability theory
    • Loeve, M.1
  • 49
    • 84971972444 scopus 로고
    • On a problem of transformations between limit-circle and limit-point differential equations
    • F. Neumann. On a problem of transformations between limit-circle and limit-point differential equations. Proc. Roy. Soc. Edinburgh Sect. A 72 (1975), 187-193.
    • (1975) Proc. Roy. Soc. Edinburgh Sect , vol.A 72 , pp. 187-193
    • Neumann, F.1
  • 50
    • 0010761458 scopus 로고
    • Singuläre S-hermitesche Rand-eigenwertprobleme
    • H. D. Niessen. Singuläre S-hermitesche Rand-eigenwertprobleme. Manuscripta Math. 3 (1970), 35-68.
    • (1970) Manuscripta Math , vol.3 , pp. 35-68
    • Niessen, H.D.1
  • 51
    • 0010717734 scopus 로고
    • Zum verallgemeinerten zweiten Weylschen Satz
    • H. D. Niessen. Zum verallgemeinerten zweiten Weylschen Satz. Arch. Math. 22 (1971), 648-656.
    • (1971) Arch. Math , vol.22 , pp. 648-656
    • Niessen, H.D.1
  • 52
    • 34250447734 scopus 로고
    • Integraltransformationen zu singulären S-Hermiteschen Randeigenwertproblemen
    • H. D. Niessen and A. Schneider. Integraltransformationen zu singulären S-Hermiteschen Randeigenwertproblemen. Manuscripta Math. 5 (1971), 133-145.
    • (1971) Manuscripta Math , vol.5 , pp. 133-145
    • Niessen, H.D.1    Schneider, A.2
  • 53
    • 0039946655 scopus 로고
    • Greensche matrix und die Formel von Titchmarsh-Kodaira für singuläre S-hermitesche Eigenwertprobleme
    • H. D. Niessen. Greensche matrix und die Formel von Titchmarsh-Kodaira für singuläre S-hermitesche Eigenwertprobleme. J. Reine Angew. Math. 261 (1973), 164-193.
    • (1973) J. Reine Angew. Math , vol.261 , pp. 164-193
    • Niessen, H.D.1
  • 54
    • 0942266071 scopus 로고
    • Operators generated by differential problems with eigenvalue parameter in equation and boundary condition
    • Jan Odhnoff. Operators generated by differential problems with eigenvalue parameter in equation and boundary condition. Meddn Lunds Univ. Mat. Semin. 14 (1959).
    • (1959) Meddn Lunds Univ. Mat. Semin , vol.14
    • Odhnoff, J.1
  • 55
    • 84952176493 scopus 로고
    • A survey of spectral theory for pairs of ordinary differential operators
    • (Berlin: Springer
    • A. Pleijel. A survey of spectral theory for pairs of ordinary differential operators. Lecture Notes in Mathematics 448, 256-272 (Berlin: Springer, 1975).
    • (1975) Lecture Notes in Mathematics , vol.448 , pp. 256-272
    • Pleijel, A.1
  • 56
    • 0001000782 scopus 로고
    • Halbbeschränkte gewöhnliche Differentialoperatoren zweiter Ordnung
    • F. Rellich. Halbbeschränkte gewöhnliche Differentialoperatoren zweiter Ordnung. Math. Ann. 122 (1951), 343-368.
    • (1951) Math. Ann , vol.122 , pp. 343-368
    • Rellich, F.1
  • 57
    • 34250508046 scopus 로고
    • Eine Bemerkung zum Weyl-Stoneschen Eigenwertproblem
    • A. Schneider. Eine Bemerkung zum Weyl-Stoneschen Eigenwertproblem. Arch. Math. 17 (1966), 352-358.
    • (1966) Arch. Math , vol.17 , pp. 352-358
    • Schneider, A.1
  • 58
    • 0010675699 scopus 로고
    • Untersuchungen über singuläre reelle S-hermitesche Differentialgleichungssysteme im Normalfall
    • A. Schneider. Untersuchungen über singuläre reelle S-hermitesche Differentialgleichungssysteme im Normalfall. Math. Z. 107 (1968), 271-296.
    • (1968) Math. Z , vol.107 , pp. 271-296
    • Schneider, A.1
  • 59
    • 34250479483 scopus 로고
    • Weitere Untersuchungen über singuläre reelle S-hermitesche Differentialgleichungssysteme im Normalfall
    • A. Schneider. Weitere Untersuchungen über singuläre reelle S-hermitesche Differentialgleichungssysteme im Normalfall. Math. Z. 109 (1969), 153-168.
    • (1969) Math. Z , vol.109 , pp. 153-168
    • Schneider, A.1
  • 60
    • 34250484427 scopus 로고
    • Die Greensche matrix S-hermitescher Rand-eigenwertprobleme im Normalfall
    • A. Schneider. Die Greensche matrix S-hermitescher Rand-eigenwertprobleme im Normalfall. Math. Ann. 180 (1969), 307-312.
    • (1969) Math. Ann , vol.180 , pp. 307-312
    • Schneider, A.1
  • 61
    • 34250491138 scopus 로고
    • Zum Entwicklungssatz bei reellen singulären Differentialgleichungs-systemen
    • A. Schneider. Zum Entwicklungssatz bei reellen singulären Differentialgleichungs-systemen. Arch. Math. 21 (1970), 192-197.
    • (1970) Arch. Math , vol.21 , pp. 192-197
    • Schneider, A.1
  • 62
    • 0011670874 scopus 로고
    • A note on eigenvalue problems with eigenvalue parameter in the boundary conditions
    • A. Schneider. A note on eigenvalue problems with eigenvalue parameter in the boundary conditions. Math. Z. 136 (1974), 163-167.
    • (1974) Math. Z , vol.136 , pp. 163-167
    • Schneider, A.1
  • 63
    • 84959804993 scopus 로고
    • On eigenfunction expansions of second-order ordinary differential equations
    • W. F. Scott. On eigenfunction expansions of second-order ordinary differential equations. J. London Math. Soc. 4 (1972), 551-559.
    • (1972) J. London Math. Soc , vol.4 , pp. 551-559
    • Scott, W.F.1
  • 64
    • 77957176332 scopus 로고
    • Integral transforms and eigenfunction theory
    • D. B. Sears. Integral transforms and eigenfunction theory. Quart. J. Math. Oxford 5 (1954), 47-58.
    • (1954) Quart. J. Math. Oxford , vol.5 , pp. 47-58
    • Sears, D.B.1
  • 67
    • 34250440396 scopus 로고
    • Regular eigenvalue problems with eigenvalue parameter in the boundary conditions
    • J. Walter. Regular eigenvalue problems with eigenvalue parameter in the boundary conditions. Math. Z. 133 (1973), 301-312.
    • (1973) Math. Z , vol.133 , pp. 301-312
    • Walter, J.1
  • 69
    • 0002268514 scopus 로고
    • Uber gewöhnliche lineare Differentialgleichungen mit Singulären Stellen und ihre Eigenfunktionen
    • H. Weyl. Uber gewöhnliche lineare Differentialgleichungen mit Singulären Stellen und ihre Eigenfunktionen. Nachr. Akad. Wiss. Göttingen Math.-Phys. Kl. II (1910), 442-467.
    • (1910) Nachr. Akad. Wiss. Göttingen Math.-Phys. Kl , vol.II , pp. 442-467
    • Weyl, H.1
  • 72
    • 33745195297 scopus 로고
    • On Titchmarsh-Kodaira's formula concerning Weyl-Stone's eigenfunction expansion
    • K. Yosida. On Titchmarsh-Kodaira's formula concerning Weyl-Stone's eigenfunction expansion. Nagoya Math. J. 1 (1950), 49-58.
    • (1950) Nagoya Math. J , vol.1 , pp. 49-58
    • Yosida, K.1
  • 74
    • 84971177113 scopus 로고
    • Su un problema al contorno per l'equazione δu + λu = 0
    • P. Zecca. Su un problema al contorno per l'equazione δu + λu = 0. Rend. Accad. Sci. Fis. Mat. Napoli 33 (1966), 279-303.
    • (1966) Rend. Accad. Sci. Fis. Mat. Napoli , vol.33 , pp. 279-303
    • Zecca, P.1


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