Eigenfunction expansions for a class of J-selfadjoint ordinary differential operators with boundary conditions containing the eigenvalue parameter

Proceedings of the Royal Society of Edinburgh: Section A Mathematics

Volumn 86, Issue 1-2, 1980, Pages 1-27

  Dijksma, Aalt ^a  

^a UNIVERSITY OF GRONINGEN   (Netherlands)

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[No Author keywords available]

Indexed keywords

EID: 84971109156     PISSN: 03082105     EISSN: 14737124     Source Type: Journal    
DOI: 10.1017/S0308210500011951     Document Type: Article

References (16)

1. J. Bognar. Indefinite inner product spaces (Berlin: Springer, 1974).
2. E. A. Coddington. Extension theory of formally normal and symmetric subspaces. Amer. Math. Soc. Memoirs 134 (1973).
3. E. A. Coddington and A. Dijksma. Adjoint subspaces in Banach spaces with applications to ordinary differential subspaces. Ann. Mat. Pura Appl. 118 (1978), 1-118.
4. D. S. Cohen. An integral transform associated with boundary conditions containing an eigenvalue parameter. SIAM J. Appl. Math. 14 (5) (1966), 1164-1175.
5. A. Dijksma and H. S. V. de Snoo. Eigenfunction expansions for nondensely defined differential operators. J. Differential Equations 17 (1975), 198-219.
6. B. Friedman. Principles and Techniques of Applied Mathematics (New York: Wiley, 1956).
7. C. T. Fulton. Two-point boundary value problems with eigenvalue parameter contained in the boundary conditions. Proc. Roy. Soc. Edinburgh Sect. A 77 (1977), 293-308.
8. B. E. Goodwin. On the realization of the eigenvalues of integral equations whose kernels are entire or meromorphic in the eigenvalue parameter. SIAM J. Appl. Math. 14 (1) (1966), 65-85.
9. I. S. Iohvidov and M. G. Krexn. Spectral theory of operators in spaces with an indefinite metric I. Amer. Math. Soc. Transl. 13 (2) (1960), 105-175.
10. M. G. Krein and H. Langer. On the spectral function of a selfadjoint operator in a space with indefinite metric. Dokl. Akad. Nauk SSSR 152 (1963), 39-42; Soviet Math. 4/13 (1963), 1236-1239.
11. H. D. Niessen. Singulare S-hermitesche Rand-Eigenwertprobleme. Manuscripta Math. 3 (1970), 35-68.
12. E. M. Russakovskii. Operator treatment of boundary problems with spectral parameters entering via polynomials in the boundary conditions. Functional Anal. Appl. 9 (1975), 358-359.
13. E. M. Russakovskii. Operator treatment of a boundary-value problem with the spectral parameter appearing rationally in the boundary conditions. Theory of functions, functional analysis and its applications 30, pp. 120-128 (Kharkov, 1978) (In Russian).
14. F. W. Schafke und A. Schneider. S-hermitesche Rand-Eigenwertprobleme I, II, III. Math. Ann. 162 (1966), 9-26; 165 (1966), 236-260; 177 (1968), 67-94.
15. A. Schneider. A note on eigenvalue problems with eigenvalue parameter in the boundary conditions. Math. Z. 136 (1974), 163-167.
16. J. Walter. Regular eigenvalue problems with eigenvalue parameter in the boundary conditions. Math. Z. 133 (1973), 301-312.