A note on polynomially growing C-0-semigroups

T. Eisner; Heiko J. Zwart

doi:10.1007/s00233-007-0723-9

A note on polynomially growing C-0-semigroups

T. Eisner
, Heiko J. Zwart

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

14 Citations (Scopus)

8 Downloads (Pure)

Abstract

We characterize polynomial growth of a $C_0$-semigroup in terms of the first power of the resolvent of its generator. We do this for a class of semigroups which includes $C_0$-semigroups on Hilbert spaces and analytic semigroups on Banach spaces. Furthermore, we characterize polynomial growth for discrete semigroups.

Original language	English
Pages (from-to)	438-445
Number of pages	8
Journal	Semigroup forum
Volume	75
Issue number	2
DOIs	https://doi.org/10.1007/s00233-007-0723-9
Publication status	Published - 2007

Keywords

C-0-semigroups
Growth estimate
Polynomially bounded

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10.1007/s00233-007-0723-9

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title = "A note on polynomially growing C-0-semigroups",

abstract = "We characterize polynomial growth of a \$C\_0\$-semigroup in terms of the first power of the resolvent of its generator. We do this for a class of semigroups which includes \$C\_0\$-semigroups on Hilbert spaces and analytic semigroups on Banach spaces. Furthermore, we characterize polynomial growth for discrete semigroups.",

keywords = "C-0-semigroups, Growth estimate, Polynomially bounded",

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T1 - A note on polynomially growing C-0-semigroups

AU - Eisner, T.

AU - Zwart, Heiko J.

PY - 2007

Y1 - 2007

N2 - We characterize polynomial growth of a $C_0$-semigroup in terms of the first power of the resolvent of its generator. We do this for a class of semigroups which includes $C_0$-semigroups on Hilbert spaces and analytic semigroups on Banach spaces. Furthermore, we characterize polynomial growth for discrete semigroups.

AB - We characterize polynomial growth of a $C_0$-semigroup in terms of the first power of the resolvent of its generator. We do this for a class of semigroups which includes $C_0$-semigroups on Hilbert spaces and analytic semigroups on Banach spaces. Furthermore, we characterize polynomial growth for discrete semigroups.

KW - C-0-semigroups

KW - Growth estimate

KW - Polynomially bounded

U2 - 10.1007/s00233-007-0723-9

DO - 10.1007/s00233-007-0723-9

M3 - Article

SN - 0037-1912

VL - 75

SP - 438

EP - 445

JO - Semigroup forum

JF - Semigroup forum

IS - 2

ER -

A note on polynomially growing C-0-semigroups

Abstract

Keywords

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