Stability of Operators and Operator Semigroups / Edition 1

by Tanja Eisner

Overview

The asymptotic behaviour, in particular "stability" in some sense, is studied systematically for discrete and for continuous linear dynamical systems on Banach spaces. Of particular concern is convergence to an equilibrium with respect to various topologies. Parallels and differences between the discrete and the continuous situation are emphasised.

Product Details

ISBN-13:	9783034803113
Publisher:	Springer Basel
Publication date:	09/07/2012
Series:	Operator Theory: Advances and Applications , #209
Edition description:	2010
Pages:	204
Product dimensions:	6.10(w) x 9.25(h) x (d)

Table of Contents

Introduction.- Chapter I. Functional analytic tools.- 1. Structure of compact semigroups.- 2. Mean ergodicity.- 3. Tools from semigroup theory.- Chapter II. Stability of linear operators.- 1. Power boundedness.- 2. Strong stability.- 3. Weak stability.- 4. Almost weak stability.- 5. Abstract examples.- 6. Stability via Lyapunov equation.- Chapter III. Stability of C0-semigroups.- 1. Boundedness.- 2. Uniform exponential stability.- 3. Strong stability.- 4. Weak stability.- 5. Almost weak stability.- 6. Abstract examples.- 7. Stability via Lyapunov equation.- Chapter IV. Discrete vs. continuous.- 1. Embedding operators into C0-semigroups.- 2. Cogenerators.- Bibliography.

Editorial Reviews

From the book reviews:

“This nice volume gives a good introduction to the asymptotic behaviour of linear dynamical systems. … This volume leads to the frontiers of recent research in a rapidly developing area of mathematics. It can be warmly recommended to researchers and graduate students interested in this field.” (László Kérchy, Acta Scientiarum Mathematicarum (Szeged), Vol. 78 (1-2), 2012)

“The author’s aim is to emphasise similarities between the discrete and continuous cases. … A reader who is new to the subject might prefer that the book included more motivational discussions … . the mathematical arguments throughout the book are presented in a style that makes them easy to follow. … it has value as a convenient reference text for comparison of the discrete and continuous cases of stability in operator theory and for exposition of links to ergodic theory.” (C. J. K. Batty, Mathematical Reviews, Issue 2011 f)

From the Publisher