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The spectrum of multiparameter problems in Hilbert space

Published online by Cambridge University Press:  14 November 2011

D. F. McGhee  and
G. F. Roach
D. F. McGhee
Affiliation:
Department of Mathematics, University of Strathclyde, Glasgow, Scotland
G. F. Roach
Affiliation:
Department of Mathematics, University of Strathclyde, Glasgow, Scotland
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Synopsis

In this paper, appropriate definitions are given for the spectra of multiparameter problems in Hilbert space when the operators involved are not necessarily self-adjoint. Notions of adjoint multiparameter problems are introduced, and some properties of the spectrum of a single linear operator are generalised to multiparameter settings.

The results which are achieved are compared with those in the literature which have beendeveloped for multiparameter problems involving self-adjoint operators.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 91 , Issue 1-2 , 1981 , pp. 31 - 42
Copyright
Copyright © Royal Society of Edinburgh 1981

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