Stability of Operators and Operator Semigroups

✍ Scribed by Tanja Eisner

Publisher: Springer Basel;Birkhäuser
Year: 2010
Tongue: English
Leaves: 208
Series: Operator Theory: Advances and Applications 209
Edition: 1st ed. 2010
Category: Library

No coin nor oath required. For personal study only.

✦ Synopsis

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.

✦ Table of Contents

Front Matter ....Pages i-xi
Functional analytic tools (Tanja Eisner)....Pages 5-35
Stability of linear operators (Tanja Eisner)....Pages 37-77
Stability of C0-semigroups (Tanja Eisner)....Pages 79-132
Connections to ergodic and measure theory (Tanja Eisner)....Pages 133-162
Discrete vs. continuous (Tanja Eisner)....Pages 163-182
Back Matter ....Pages 183-204

✦ Subjects

Mathematics; Operator Theory; Dynamical Systems and Ergodic Theory; Systems Theory, Control

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