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＜電子ブック＞
Stability of Operators and Operator Semigroups / by Tanja Eisner
(Operator Theory: Advances and Applications. ISSN:22964878 ; 209)

版	1st ed. 2010.
出版者	(Basel : Springer Basel : Imprint: Birkhäuser)
出版年	2010
本文言語	英語
大きさ	VII, 204 p. 8 illus : online resource
著者標目	*Eisner, Tanja author SpringerLink (Online service)
件　名	LCSH:Operator theory LCSH:Dynamical systems LCSH:System theory LCSH:Control theory FREE:Operator Theory FREE:Dynamical Systems FREE:Systems Theory, Control
一般注記	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 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 HTTP:URL=https://doi.org/10.1007/978-3-0346-0195-5

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