This book systematically studies the asymptotic behavior, in particular "stability" in some sense, for discrete and continuous linear dynamical systems on Banach spaces. Of special concern is convergence to an equilibrium regarding various topologies. Series: Operator Theory: Advances and Applications. Num Pages: 212 pages, 1 colour illustrations, biography. BIC Classification: GPFC; PBKF; PBWR. Category: (P) Professional & Vocational. Dimension: 234 x 156 x 11. Weight in Grams: 307. . 2012. Paperback. . . . .

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Bibliographic Details

Title: Stability of Operators and Operator Semigroups
Publisher: Springer Basel
Publication Date: 2012
Language: English
ISBN 10: 3034803117
ISBN 13: 9783034803113
Binding: Soft cover
Condition: New

About this title

Synopsis

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.

From the Back Cover

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.

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