Mean stability of semigroups

Shmuel Kantorovitz; Serguei Piskarev

doi:10.11650/twjm/1500407402

Mean stability of semigroups

Shmuel Kantorovitz
, Serguei Piskarev

Department of Mathematics

Lomonosov Moscow State University

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

2 Scopus citations

Abstract

Let T(·) be a bounded C₀-semigroup on the Banach space X, with generator A. It is shown that the denseness of range A is necessary and sufficient for the semigroup's mean stability with respect to suitable weights. Analogous results are valid for power bounded operators, tensor product semigroups, and cosine operator functions.

Original language	English
Pages (from-to)	89-103
Number of pages	15
Journal	Taiwanese Journal of Mathematics
Volume	6
Issue number	1
DOIs	https://doi.org/10.11650/twjm/1500407402
State	Published - Mar 2002

Keywords

C-semigroup
Cosine operator function
Generator
Mean stability
Point spectrum
Power bounded operator
Residual spectrum
Semigroup
Tensor product of semigroups

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10.11650/twjm/1500407402

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KW - Cosine operator function

KW - Generator

KW - Mean stability

KW - Point spectrum

KW - Power bounded operator

KW - Residual spectrum

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KW - Tensor product of semigroups

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Mean stability of semigroups

Abstract

Keywords

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