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Eigenfunction expansions for nondensely defined differential operators. (English) Zbl 0299.47023


MSC:

47B25 Linear symmetric and selfadjoint operators (unbounded)
34L99 Ordinary differential operators
47E05 General theory of ordinary differential operators
47A70 (Generalized) eigenfunction expansions of linear operators; rigged Hilbert spaces
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[1] Achieser, N. I.; Glasmann, I. M., Theorie der linearen Operatoren im Hilbert-Raum (1968), Akademie-Verlag: Akademie-Verlag Berlin · Zbl 0056.11101
[2] Bourbaki, N., Intégration (1959), Hermann: Hermann Paris, Fasc. 25 · Zbl 0189.14201
[3] Coddington, E. A., Extension theory of formally normal and symmetric subspaces, Mem. Amer. Math. Soc., 134 (1973) · Zbl 0265.47023
[4] Coddington, E. A., Self-adjoint subspace extensions of non-densely defined symmetric operators, Bull. Amer. Math. Soc., 79, 712-715 (1973) · Zbl 0285.47020
[5] Coddington, E. A., Self-adjoint subspace extensions of non-densely defined symmetric operators, Advances in Math., 14, 309-332 (1974) · Zbl 0307.47028
[6] Coddington, E. A., Eigenfunction expansions for non-densely defined symmetric operators, Bull. Amer. Math. Soc., 79, 964-968 (1973) · Zbl 0285.47021
[7] Coddington, E. A., Self-adjoint problems for non-densely defined ordinary differential operators and their eigenfunction expansions, Advances in Math., 15 (1975) · Zbl 0307.47029
[8] Dijksma, A.; de Snoo, H. S.V, Integral transforms and a class of singular \(S\)-hermitian eigenvalue problems, Manuscripta Math., 10, 129-139 (1973) · Zbl 0268.34032
[9] Hirschfeld, R. A., Expansions in eigenfunctionals, (Proc. Kon. Ned. Ak. Wet., 68 (1965)), 513-520 · Zbl 0143.16401
[10] Niessen, H.-D, Singuläre \(S\)-hermitesche Rand-Eigenwertprobleme, Manuscripta Math., 3, 35-68 (1970) · Zbl 0195.37603
[11] Rellich, F., Spectral theory of a second order ordinary differential operator (1950-1951), New York University
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