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Generalized resolvents of ordinary differential operators
Authors:
Earl A. Coddington and Richard C. Gilbert
Journal:
Trans. Amer. Math. Soc. 93 (1959), 216-241
MSC:
Primary 47.60; Secondary 34.30
MathSciNet review:
0163192
Full-text PDF Free Access
References |
Similar Articles |
Additional Information
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N.
I. Achieser and I.
M. Glasmann, Theorie der linearen Operatoren im Hilbert-Raum,
Akademie-Verlag, Berlin, 1954 (German). MR 0066560
(16,596f)
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N.
Bourbaki, Eléments de mathématique. XV.
Première partie: Les structures fondamentales de l’analyse.
Livre V: Espaces vectoriels topologiques. Chapitre I: Espaces vectoriels
topologiques sur un corps valué. Chapitre II: Ensembles convexes et
espaces localement convexes, Actualités Sci. Ind., no. 1189,
Herman & Cie, Paris, 1953 (French). MR 0054161
(14,880b)
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Earl
A. Coddington, On maximal symmetric ordinary differential
operators, Math. Scand. 4 (1956), 22–28. MR 0084748
(18,915c)
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Earl
A. Coddington, Generalized resolutions of the identity for closed
symmetric ordinary differential operators, Proc. Nat. Acad. Sci.
U.S.A. 42 (1956), 638–642. MR 0084749
(18,915d)
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Earl
A. Coddington, Generalized resolutions of the identity for
symmetric ordinary differential operators, Ann. of Math. (2)
68 (1958), 378–392. MR 0103319
(21 #2094)
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Einar
Hille and Ralph
S. Phillips, Functional analysis and semi-groups, American
Mathematical Society Colloquium Publications, vol. 31, American
Mathematical Society, Providence, R. I., 1957. rev. ed. MR 0089373
(19,664d)
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N.
Levinson, Transform and inverse transform expansions for singular
self-adjoint differential operators, Illinois J. Math.
2 (1958), 224–235. MR 0096850
(20 #3332)
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M.
Neumark, Spectral functions of a symmetric operator, Bull.
Acad. Sci. URSS. Sér. Math. [Izvestia Akad. Nauk SSSR]
4 (1940), 277–318 (Russian, with English summary).
MR
0002714 (2,105a)
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M.
A. Neumark, Extremal spectral functions of a symmetric
operator, Bull. Acad. Sci. URSS. Sér. Math. [Izvestia Akad.
Nauk SSSR] 11 (1947), 327–344 (Russian, with English
summary). MR
0024062 (9,447b)
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A.
V. Štraus, Generalized resolvents of symmetric
operators, Izvestiya Akad. Nauk SSSR. Ser. Mat. 18
(1954), 51–86 (Russian). MR 0062954
(16,48e)
- [1]
- N. I. Achieser and I. M. Glasmann, Theorie der linearen Operatoren im Hilbert-Raum, Akademie Verlag, Berlin, 1954 (German translation). MR 0066560 (16:596f)
- [2]
- N. Bourbaki, Espaces vectoriels topologiques, Éléments de Mathématique, A. S. I. 1189, Hermann et Cie, Paris, 1953. MR 0054161 (14:880b)
- [3]
- E. A. Coddington, On maximal symmetric ordinary differential operators, Math. Scand. vol. 4 (1956) pp. 22-28. MR 0084748 (18:915c)
- [4]
- -, Generalized resolutions of the identity for closed symmetric ordinary differential operators, Proc. Nat. Acad. Sci. U.S.A. vol. 42 (1956) pp. 638-642. MR 0084749 (18:915d)
- [5]
- -, Generalized resolutions of the identity for symmetric ordinary differential operators, Ann. of Math. vol. 68 (1958) pp. 378-392. MR 0103319 (21:2094)
- [6]
- E. Hille and R. S. Phillips, Functional analysis and semi-groups, Amer. Math. Soc. Colloquium Publications, vol. 31, 1957. MR 0089373 (19:664d)
- [7]
- N. Levinson, Transform and inverse transform expansions for singular self-adjoint differential operators, Illinois J. Math. vol. 2 (1958) pp. 224-235. MR 0096850 (20:3332)
- [8]
- M. A. Naimark, Spectral functions of a symmetric operator, Izv. Akad. Nauk SSSR. Ser. Mat. vol. 4 (1940) pp. 277-318. MR 0002714 (2:105a)
- [9]
- -, Extremal spectral functions of symmetric operators, Izv. Akad. Nauk SSSR. Ser. Mat. vol. 11 (1947) pp. 327-344. MR 0024062 (9:447b)
- [10]
- A. V. Štraus, Generalized resolvents of symmetric operators, Izv. Akad. Nauk SSSR. Ser. Mat. vol. 18 (1954) pp. 51-86. MR 0062954 (16:48e)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S0002-9947-1959-0163192-9
PII:
S 0002-9947(1959)0163192-9
Article copyright:
© Copyright 1959 American Mathematical Society
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