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Coupled operator systems and multiparameter spectral theory*

Published online by Cambridge University Press:  14 November 2011

G. F. Roach  and
B. D. Sleeman
G. F. Roach
Affiliation:
Department of Mathematics, University of Strathclyde
B. D. Sleeman
Affiliation:
Department of Mathematics, University of Dundee
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Synopsis

In this paper a spectral theory for completely coupled linear operator systems is developed. These systems take the form

where Ak, Bk are n × n matrices with operator entries. Λ is an n × n matrix with complex scalar entries and xk is an n × 1 column vector. The main result is a Parseval equality and expansion theorem.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 80 , Issue 1-2 , 1978 , pp. 23 - 34
Copyright
Copyright © Royal Society of Edinburgh 1978

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