An abstract multiparameter spectral theory-Reference-Cited by-同舟云学术

An abstract multiparameter spectral theory

Published:1982 Issue:3-4 Volume:92 Page:193-204
ISSN:0308-2105
Container-title:Proceedings of the Royal Society of Edinburgh: Section A Mathematics
language:en
Short-container-title:Proceedings of the Royal Society of Edinburgh: Section A Mathematics

Author:

Binding P. A.,Källström A.,Sleeman B. D.

Abstract

SynopsisWe consider the eigenvalue problem

for self-adjoint operators Ai and Bij on separable Hilbert spaces Hi. It is assumed that and Bij are bounded with compact. Various properties of the eigentuples λi, and xi are deduced under a “definiteness condition” weaker than those used by previous authors, at least in infinite dimensions. In particular, a Parseval relation and eigenvector expansion are derived in a suitably constructed tensor product space.

Publisher

Cambridge University Press (CUP)

Subject

General Mathematics

Reference18 articles.

1. An abstract multiparameter spectral theory;Källström;Univ. of Dundee Math. Report 75,1975

2. The completeness and expansion theorems associated with the multi-parameter eigenvalue problem in ordinary differential equations

3. 3On a problem of B. D. Sleeman. J. Math. Anal. Appl, to appear.

4. Abstract multiparameter theory, II

5. A multi-parameter eigenvalue problem

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