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© 2010

Stability of Operators and Operator Semigroups

  • Joint treatment of discrete and continuous systems

  • Careful investigation of the behavior with respect to different topologies on infinite dimensional spaces

Book

Part of the Operator Theory: Advances and Applications book series (OT, volume 209)

Table of contents

  1. Front Matter
    Pages i-xi
  2. Tanja Eisner
    Pages 5-35
  3. Tanja Eisner
    Pages 37-77
  4. Tanja Eisner
    Pages 79-132
  5. Tanja Eisner
    Pages 133-162
  6. Tanja Eisner
    Pages 163-182
  7. Back Matter
    Pages 183-204

About this book

Introduction

This book is about stability of linear dynamical systems, discrete and continuous. More precisely, we discuss convergence to zero of strongly continuous semigroups of operators and of powers of a bounded linear operator, both with respect to different topologies. The discrete and the continuous cases are treated in parallel, and we systematically employ a comparison of methods and results in either case. Apart from classical results, many recent crucial developments in the area are presented, such as the resolvent approach to stability. Special attention is payed to stability with respect to the weak operator topology. We also connect stability in operator theory to its analogues in ergodic theory and harmonic analysis. The book is addressed to all researchers and graduate students interested in this field.

Keywords

Group theory dynamical systems stability

Authors and affiliations

  1. 1.Arbeitsbereich FunktionalanalysisMathematisches InstitutTübingenGermany

Bibliographic information

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)