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10.—An Abstract Relation for Multiparameter Eigenvalue Problems*

Published online by Cambridge University Press:  14 February 2012

A. Källström  and
B. D. Sleeman
A. Källström
Affiliation:
Department of Mathematics, University of Dundee.
B. D. Sleeman
Affiliation:
Department of Mathematics, University of Dundee.
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Synopsis

Consider the multiparameter system

where ut is an element of a separable Hilbert space Hi, i = 1, …, n. The operators Sij are assumed to be bounded symmetric operators in Hi and Ai is assumed self-adjoint. In addition consider the operator equation

where B is densely defined and closed in a separable Hilbert space H and Tj, j = 1, …, n is a bounded operator in H. The problem treated in this paper is to seek an expression for a solution v of (**) in terms of the eigenfunctions of the system (*).

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 74 , 1976 , pp. 135 - 143
Copyright
Copyright © Royal Society of Edinburgh 1976

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