The Cayley transform of the generator of a bounded C0-semigroup

A. Gomilko; Heiko J. Zwart

doi:10.1007/s00233-006-0648-8

The Cayley transform of the generator of a bounded C₀-semigroup

A. Gomilko
, Heiko J. Zwart

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

5 Citations (Scopus)

7 Downloads (Pure)

Abstract

Let $A$ be the generator of a uniformly bounded $C_0$-semigroup on the Banach space $X$. We present sufficient conditions on the resolvent $(A-\lambda I)^{-1},$ $Re(\lambda)>0,$ under which the Cayley transform $V=(A+I)(A-I)^{-1}$ is a power-bounded operator, i.e., $\sup_{n\in N}\,\|V^n\|\,<\infty.$

Original language	Undefined
Article number	10.1007/s00233-006-0648-8
Pages (from-to)	140-148
Number of pages	9
Journal	Semigroup forum
Volume	74
Issue number	1/1
DOIs	https://doi.org/10.1007/s00233-006-0648-8
Publication status	Published - Feb 2007

Keywords

MSC-93C25
IR-63698
EWI-8191
METIS-241701

Access to Document

10.1007/s00233-006-0648-8

http://eprints.eemcs.utwente.nl/secure2/8191/01/gzc1-semigroup.pdf

Cite this

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title = "The Cayley transform of the generator of a bounded C0-semigroup",

abstract = "Let \$A\$ be the generator of a uniformly bounded \$C\_0\$-semigroup on the Banach space \$X\$. We present sufficient conditions on the resolvent \$(A-\textbackslash{}lambda I)\textasciicircum{}\{-1\},\$ \$Re(\textbackslash{}lambda)>0,\$ under which the Cayley transform \$V=(A+I)(A-I)\textasciicircum{}\{-1\}\$ is a power-bounded operator, i.e., \$\textbackslash{}sup\_\{n\textbackslash{}in N\}\textbackslash{},\textbackslash{}|V\textasciicircum{}n\textbackslash{}|\textbackslash{},<\textbackslash{}infty.\$",

keywords = "MSC-93C25, IR-63698, EWI-8191, METIS-241701",

author = "A. Gomilko and Zwart, \{Heiko J.\}",

note = "10.1007/s00233-006-0648-8 ",

year = "2007",

month = feb,

doi = "10.1007/s00233-006-0648-8",

language = "Undefined",

volume = "74",

pages = "140--148",

journal = "Semigroup forum",

issn = "0037-1912",

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T1 - The Cayley transform of the generator of a bounded C0-semigroup

AU - Gomilko, A.

AU - Zwart, Heiko J.

N1 - 10.1007/s00233-006-0648-8

PY - 2007/2

Y1 - 2007/2

N2 - Let $A$ be the generator of a uniformly bounded $C_0$-semigroup on the Banach space $X$. We present sufficient conditions on the resolvent $(A-\lambda I)^{-1},$ $Re(\lambda)>0,$ under which the Cayley transform $V=(A+I)(A-I)^{-1}$ is a power-bounded operator, i.e., $\sup_{n\in N}\,\|V^n\|\,<\infty.$

AB - Let $A$ be the generator of a uniformly bounded $C_0$-semigroup on the Banach space $X$. We present sufficient conditions on the resolvent $(A-\lambda I)^{-1},$ $Re(\lambda)>0,$ under which the Cayley transform $V=(A+I)(A-I)^{-1}$ is a power-bounded operator, i.e., $\sup_{n\in N}\,\|V^n\|\,<\infty.$

KW - MSC-93C25

KW - IR-63698

KW - EWI-8191

KW - METIS-241701

U2 - 10.1007/s00233-006-0648-8

DO - 10.1007/s00233-006-0648-8

M3 - Article

SN - 0037-1912

VL - 74

SP - 140

EP - 148

JO - Semigroup forum

JF - Semigroup forum

IS - 1/1

M1 - 10.1007/s00233-006-0648-8

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