Stability of Operators and Operator Semigroups
Author:   Tanja Eisner
Publisher:   Springer Basel
Edition:   2010 ed.
Volume:   209
ISBN:  

9783034803113


Pages:   204
Publication Date:   07 September 2012
Format:   Paperback
Availability:   Manufactured on demand   Availability explained
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Stability of Operators and Operator Semigroups


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.

Full Product Details

Author:   Tanja Eisner
Publisher:   Springer Basel
Imprint:   Springer Basel
Edition:   2010 ed.
Volume:   209
Dimensions:   Width: 15.50cm , Height: 1.10cm , Length: 23.50cm
Weight:   0.454kg
ISBN:  

9783034803113


ISBN 10:   3034803117
Pages:   204
Publication Date:   07 September 2012
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   Manufactured on demand   Availability explained
We will order this item for you from a manufactured on demand supplier.

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.

Reviews

From the reviews: 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)


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