The growth of a semigroup and its Cayley transform

N.C. Besseling; Heiko J. Zwart

The growth of a semigroup and its Cayley transform

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Abstract

Let $A$ be the infinitesimal generator of an exponentially stable, strongly continuous semigroup on a Hilbert space. We show that the powers of the Cayley transform of $A$ are bounded by a constant times $\log (n+1)$. The proof is based on Lyapunov equations.

Original language	Undefined
Place of Publication	Enschede
Publisher	University of Twente
Number of pages	9
Publication status	Published - Apr 2011

Publication series

Name
Publisher	Department of Applied Mathematics, University of Twente
No.	1941
ISSN (Print)	1874-4850
ISSN (Electronic)	1874-4850

Keywords

MSC-34G10
IR-76707
METIS-278712
MSC-39A11
MSC-46N20
EWI-20080

Access to Document

http://www.math.utwente.nl/publications

Cite this

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title = "The growth of a semigroup and its Cayley transform",

abstract = "Let $A$ be the infinitesimal generator of an exponentially stable, strongly continuous semigroup on a Hilbert space. We show that the powers of the Cayley transform of $A$ are bounded by a constant times $\log (n+1)$. The proof is based on Lyapunov equations.",

keywords = "MSC-34G10, IR-76707, METIS-278712, MSC-39A11, MSC-46N20, EWI-20080",

author = "N.C. Besseling and Zwart, {Heiko J.}",

year = "2011",

month = apr,

language = "Undefined",

publisher = "University of Twente",

number = "1941",

address = "Netherlands",

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TY - BOOK

T1 - The growth of a semigroup and its Cayley transform

AU - Besseling, N.C.

AU - Zwart, Heiko J.

PY - 2011/4

Y1 - 2011/4

N2 - Let $A$ be the infinitesimal generator of an exponentially stable, strongly continuous semigroup on a Hilbert space. We show that the powers of the Cayley transform of $A$ are bounded by a constant times $\log (n+1)$. The proof is based on Lyapunov equations.

AB - Let $A$ be the infinitesimal generator of an exponentially stable, strongly continuous semigroup on a Hilbert space. We show that the powers of the Cayley transform of $A$ are bounded by a constant times $\log (n+1)$. The proof is based on Lyapunov equations.

KW - MSC-34G10

KW - IR-76707

KW - METIS-278712

KW - MSC-39A11

KW - MSC-46N20

KW - EWI-20080

M3 - Report

BT - The growth of a semigroup and its Cayley transform

PB - University of Twente

CY - Enschede

ER -