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An abstract multiparameter spectral theory

Published online by Cambridge University Press:  14 November 2011

P. A. Binding ,
A. Källström  and
B. D. Sleeman
P. A. Binding
Affiliation:
Department of Mathematics and Statistics, University of Calgary, Calgary, Alberta, CanadaT2N 1N4
A. Källström
Affiliation:
Department of Mathematics, Uppsala University, S-75238 Uppsala, Sweden
B. D. Sleeman
Affiliation:
Department of Mathematical Sciences, University of Dundee, Dundee DD1 4HN, Scotland
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Synopsis

We 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.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 92 , Issue 3-4 , 1982 , pp. 193 - 204
Copyright
Copyright © Royal Society of Edinburgh 1982

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