The Asymptotic Behaviour of Semigroups of Linear Operators (Operator Theory Advances and Applications)

 
9780817654559: The Asymptotic Behaviour of Semigroups of Linear Operators (Operator Theory Advances and Applications)

Over the past ten years, the asymptotic theory of one-parameter semigroups of operators has witnessed an explosive development. A number oflong-standing open problems have recently been solved and the theory seems to have obtained a certain degree of maturity. These notes, based on a course delivered at the University of Tiibingen in the academic year 1994-1995, represent a first attempt to organize the available material, most of which exists only in the form of research papers. If A is a bounded linear operator on a complex Banach space X, then it is an easy consequence of the spectral mapping theorem exp(tO"(A)) = O"(exp(tA)), t E JR, and Gelfand's formula for the spectral radius that the uniform growth bound of the wt family {exp(tA)h o, i. e. the infimum of all wE JR such that II exp(tA)II:::: Me for some constant M and all t 2: 0, is equal to the spectral bound s(A) = sup{Re A: A E O"(A)} of A. This fact is known as Lyapunov's theorem. Its importance resides in the fact that the solutions of the initial value problem du(t) =A () dt u t, u(O) = x, are given by u(t) = exp(tA)x. Thus, Lyapunov's theorem implies that the expo- nential growth of the solutions of the initial value problem associated to a bounded operator A is determined by the location of the spectrum of A.

Les informations fournies dans la section « Synopsis » peuvent faire référence à une autre édition de ce titre.

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Jan Van Neerven
Edité par Birkhauser (1996)
ISBN 10 : 0817654550 ISBN 13 : 9780817654559
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Description du livre Birkhauser, 1996. Hardcover. État : New. book. N° de réf. du libraire M0817654550

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Acheter neuf
EUR 108,24
Autre devise

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Frais de port : Gratuit
Vers Etats-Unis
Destinations, frais et délais