Stability of Operators and Operator Semigroups
(Sprache: Englisch)
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...
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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.
Klappentext zu „Stability of Operators and Operator Semigroups “
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.
Inhaltsverzeichnis zu „Stability of Operators and Operator Semigroups “
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 C 0 -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 C 0 -semigroups.- 2. Cogenerators.- Bibliography.Bibliographische Angaben
- Autor: Tanja Eisner
- 2010, 2010, 204 Seiten, Maße: 17,3 x 24,6 cm, Gebunden, Englisch
- Verlag: Springer
- ISBN-10: 3034601948
- ISBN-13: 9783034601948
- Erscheinungsdatum: 15.07.2010
Sprache:
Englisch
Rezension zu „Stability of Operators and Operator Semigroups “
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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