A comparison theorem for selfadjoint operators

Author:
Amin Boumenir

Journal:
Proc. Amer. Math. Soc. **111** (1991), 161-175

MSC:
Primary 47B25; Secondary 34L40, 47A70, 47E05

MathSciNet review:
1021896

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: In this work we shall establish a result concerning the spectral theory of differential operators. Let and be two self-adjoint operators acting in two different Hubert spaces. Then under some conditions we shall prove that

**[1]**Aleksandrjian,*Spectral decomposition of arbitrary self-adjoint operators into eigenfunctionals*, Soviet Mat.**5**(1985), 607-611.**[2]**W. N. Everitt and A. Zettl,*On a class of integral inequalities*, J. London Math. Soc. (2)**17**(1978), no. 2, 291–303. MR**0477234****[3]**I. M. Gel′fand and A. G. Kostyučenko,*Expansion in eigenfunctions of differential and other operators*, Dokl. Akad. Nauk SSSR (N.S.)**103**(1955), 349–352 (Russian). MR**0073136****[4]**I. M. Gel′fand and B. M. Levitan,*On the determination of a differential equation from its spectral function*, Amer. Math. Soc. Transl. (2)**1**(1955), 253–304. MR**0073805****[5]**I.M. Gelfand and G. E. Shilov,*Generalized functions*, vols. 2-4, Academic Press, New York, 1961. (English transl.)**[6]**Seymour Goldberg,*Unbounded linear operators: Theory and applications*, McGraw-Hill Book Co., New York-Toronto, Ont.-London, 1966. MR**0200692****[7]**K. Maurin,*General eigenfunctions expansions*, Polska. Akad. Nauk.**48**(1969).**[9]**N. Naimark,*Linear differential operators*, Part 2, Ungar, New York, 1968. (English transl.)**[10]**A. I. Plesner and V. A. Rohlin,*Spectral theory of linear operators*, Amer. Math. Soc. Transl. (2)**62**(1946), 24-101.**[11]**J. Weidman,*Spectral theory of differential operators*, Lecture Notes in Math., vol. 1258, Springer-Verlag.

Retrieve articles in *Proceedings of the American Mathematical Society*
with MSC:
47B25,
34L40,
47A70,
47E05

Retrieve articles in all journals with MSC: 47B25, 34L40, 47A70, 47E05

Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1991-1021896-3

Article copyright:
© Copyright 1991
American Mathematical Society