Growth estimates for $\exp(A^{-1}t)$ on a Hilbert space

Hans Zwart

doi:10.1007/s00233-006-0679-1

Growth estimates for $\exp(A^{-1}t)$ on a Hilbert space

Hans Zwart

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

8 Citations (Scopus)

Abstract

Let $A$ be the infinitesimal generator of an exponentially stable, strongly continuous semigroup on the Hilbert space $H$. Since $A^{-1}$ is a bounded operator, it is the infinitesimal generator of a strongly continuous semigroup. In this paper we show that the growth of this semigroup is bounded by a constant times $\log(t)$.

Original language	English
Pages (from-to)	487-494
Number of pages	8
Journal	Semigroup forum
Volume	74
Issue number	3
DOIs	https://doi.org/10.1007/s00233-006-0679-1
Publication status	Published - 2007

Keywords

MSC-47D06
EWI-11962
IR-62177
METIS-247054

Access to Document

10.1007/s00233-006-0679-1

http://eprints.eemcs.utwente.nl/secure2/11962/01/semfor74.pdf

Cite this

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title = "Growth estimates for $\exp(A^{-1}t)$ on a Hilbert space",

abstract = "Let $A$ be the infinitesimal generator of an exponentially stable, strongly continuous semigroup on the Hilbert space $H$. Since $A^{-1}$ is a bounded operator, it is the infinitesimal generator of a strongly continuous semigroup. In this paper we show that the growth of this semigroup is bounded by a constant times $\log(t)$.",

keywords = "MSC-47D06, EWI-11962, IR-62177, METIS-247054",

author = "Hans Zwart",

note = "10.1007/s00233-006-0679-1 ",

year = "2007",

doi = "10.1007/s00233-006-0679-1",

language = "English",

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pages = "487--494",

journal = "Semigroup forum",

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TY - JOUR

T1 - Growth estimates for $\exp(A^{-1}t)$ on a Hilbert space

AU - Zwart, Hans

N1 - 10.1007/s00233-006-0679-1

PY - 2007

Y1 - 2007

N2 - Let $A$ be the infinitesimal generator of an exponentially stable, strongly continuous semigroup on the Hilbert space $H$. Since $A^{-1}$ is a bounded operator, it is the infinitesimal generator of a strongly continuous semigroup. In this paper we show that the growth of this semigroup is bounded by a constant times $\log(t)$.

AB - Let $A$ be the infinitesimal generator of an exponentially stable, strongly continuous semigroup on the Hilbert space $H$. Since $A^{-1}$ is a bounded operator, it is the infinitesimal generator of a strongly continuous semigroup. In this paper we show that the growth of this semigroup is bounded by a constant times $\log(t)$.

KW - MSC-47D06

KW - EWI-11962

KW - IR-62177

KW - METIS-247054

U2 - 10.1007/s00233-006-0679-1

DO - 10.1007/s00233-006-0679-1

M3 - Article

SN - 0037-1912

VL - 74

SP - 487

EP - 494

JO - Semigroup forum

JF - Semigroup forum

IS - 3

ER -