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The closure of the generalised eigenspace of a class of infinitesimal generators

Published online by Cambridge University Press:  14 November 2011

S. M. Verduyn Lunel
S. M. Verduyn Lunel
Affiliation:
School of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332, U.S.A and Faculteit Wiskunde en Informatica, Vrije Universiteit, de Boelelaan 1081a, 1081 HV Amsterdam, The Netherlands
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Synopsis

In this paper we study the fine geometric structure of a class of strongly continuous semigroups that satisfy the following property: the resolvent of the infinitesimal generator can be represented as the quotient of entire functions of finite exponential type. This class includes the solution map for functional differential equations and certain partial differential equations. In particular, we present necessary and sufficient conditions for one-to-oneness of the solution map and for completeness of the system of generalised eigenfunctions of the generator.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 117 , Issue 1-2 , 1991 , pp. 171 - 192
Copyright
Copyright © Royal Society of Edinburgh 1991

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