The Growth Bound for Strongly Continuous Semigroups on Fréchet Spaces

Sven Ake Wegner

doi:10.1017/S0013091515000310

The Growth Bound for Strongly Continuous Semigroups on Fréchet Spaces

Sven Ake Wegner

SCEDT Engineering

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

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.

Original language	English
Pages (from-to)	801-810
Number of pages	10
Journal	Proceedings of the Edinburgh Mathematical Society
Volume	59
Issue number	3
DOIs	https://doi.org/10.1017/S0013091515000310
Publication status	E-pub ahead of print - 23 Nov 2015

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10.1017/S0013091515000310

https://arxiv.org/abs/1408.5037Licence: CC BY-NC-ND

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abstract = "We introduce the concepts of growth and spectral bound for strongly continuous semigroups acting on Fr{\'e}chet 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 Fr{\'e}chet spaces effects with respect to these bounds may happen that cannot occur on a Banach space.",

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AB - 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.

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The Growth Bound for Strongly Continuous Semigroups on Fréchet Spaces

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