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The Growth Bound for Strongly Continuous Semigroups on Fréchet Spaces

Part of: Differential equations in abstract spaces Groups and semigroups of linear operators, their generalizations and applications Topological linear spaces and related structures

Published online by Cambridge University Press:  23 November 2015

Sven-Ake Wegner
Sven-Ake Wegner*
Affiliation:
Sobolev Institute of Mathematics, Pr. Akad. Koptyuga 4, 630090, Novosibirsk, Russia (wegner@math.uni-wuppertal.de)
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Abstract

We introduce the concepts of growth and spectral bound for strongly continuous semigroups acting on Fréchet spaces and show that the Banach space inequality s(A) ⩽ ω 0(T) extends to the new setting. Via a concrete example of an even uniformly continuous semigroup, we illustrate that for Fréchet spaces effects with respect to these bounds may happen that cannot occur on a Banach space.

Keywords

semigroupgrowth boundspectral boundpower-bounded operatorFréchet space

MSC classification

Secondary: 47D06: One-parameter semigroups and linear evolution equations 46A04: Locally convex Fréchet spaces and (DF)-spaces 34G10: Linear equations
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 59 , Issue 3 , August 2016 , pp. 801 - 810
Copyright
Copyright © Edinburgh Mathematical Society 2015 

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