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Stability of Operators and Operator Semigroups de Tanja Eisner

Stability of Operators and Operator Semigroups: Operator Theory: Advances and Applications, cartea 209

Autor Tanja Eisner
en Limba Engleză Paperback – 7 sep 2012
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.
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Specificații

ISBN-13: 9783034803113
ISBN-10: 3034803117
Pagini: 212
Ilustrații: VII, 204 p. 8 illus.
Dimensiuni: 155 x 235 x 11 mm
Greutate: 0.27 kg
Ediția:2010
Editura: Springer
Colecția Birkhäuser
Seria Operator Theory: Advances and Applications

Locul publicării:Basel, Switzerland

Public țintă

Research

Cuprins

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.

Recenzii

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)

Textul de pe ultima copertă

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.

Caracteristici

Joint treatment of discrete and continuous systems Careful investigation of the behavior with respect to different topologies on infinite dimensional spaces Includes supplementary material: sn.pub/extras