The Asymptotic Behaviour of Semigroups of Linear Operators (Hardcover, 1996 ed.)

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.

General

Imprint:	Birkhauser Verlag AG
Country of origin:	Switzerland
Series:	Operator Theory: Advances and Applications, 88
Release date:	July 1996
First published:	July 1996
Authors:	Jan Van Neerven
Dimensions:	235 x 155 x 15mm (L x W x T)
Format:	Hardcover
Pages:	241
Edition:	1996 ed.
ISBN-13:	978-3-7643-5455-8
Categories:	Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Functional analysis Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Differential equations
LSN:	3-7643-5455-0
Barcode:	9783764354558

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