The Asymptotic Behaviour of Semigroups of Linear Operators

Language: English

Published by Birkhäuser, Birkhäuser Okt 2011, 2011

3034899440 / 9783034899444

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This item is printed on demand - Print on Demand Titel. Neuware -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.Springer Nature c/o IBS, Benzstrasse 21, 48619 Heek 256 pp. Englisch.

Seller Inventory # 9783034899444

Title
The Asymptotic Behaviour of Semigroups of Linear Operators
Author
Jan Van Neerven
Publisher
Birkhäuser, Birkhäuser Okt 2011
Publication year
2011
Condition
Neu
Binding
Taschenbuch
Language
English
ISBN 10
3034899440
ISBN 13
9783034899444
Item weight
394 grams
Dimensions
235x155x15 mm

buchversandmimpf2000

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