Stability of Operators and Operator Semigroups

Eisner, Tanja

ISBN 10: 3034803117 / ISBN 13: 9783034803113

Editore: Birkhauser 2012-09, 2012

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Codice articolo 6666-IUK-9783034803113

Dati bibliografici

• Titolo: Stability of Operators and Operator Semigroups
• Editore: Birkhauser 2012-09
• Data di pubblicazione: 2012
• Lingua: Inglese
• ISBN 10: 3034803117
• ISBN 13: 9783034803113
• Rilegatura: PF
• Condizione: New

Descrizione articolo

Riassunto

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.

Dalla quarta di copertina

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.