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: (UP) Postgraduate, Research & Scholarly. Dimension: 244 x 170 x 14. Weight in Grams: 548. . 2010. Hardback. . . . . Books ship from the US and Ireland.

Bestandsnummer des Verk�ufers V9783034601948

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Titel: Stability of Operators and Operator Semigroups
Verlag: Birkhauser Verlag AG
Erscheinungsjahr: 2010
Sprache: Englisch
ISBN-10: 3034601948
ISBN-13: 9783034601948
Einband: Hardcover
Zustand: New

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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.

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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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