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The Asymptotic Behaviour of Semigroups of Linear Operators (Operator Theory: Advances and Applications, 88)

Neerven, Jan Van

Edit� par Birkh�user, 1996

ISBN 10 : 3764354550 ISBN 13 : 9783764354558

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Etat : New. N� de r�f. du vendeur ABLIING23Apr0316110058796

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The Asymptotic Behaviour of Semigroups of Linear Operators

Jan Van Neerven

Edit� par Birkh�user Basel, 1996

ISBN 10 : 3764354550 ISBN 13 : 9783764354558

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Etat : Sehr gut. Zustand: Sehr gut - Gepflegter, sauberer Zustand. | Seiten: 256 | Sprache: Englisch | Produktart: B�cher. N� de r�f. du vendeur 624567/2

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The Asymptotic Behaviour of Semigroups of Linear Operators (Operator Theory: Advances and Applications, 88)

Neerven, Jan Van

Edit� par Birkh�user, 1996

ISBN 10 : 3764354550 ISBN 13 : 9783764354558

Neuf Couverture rigide

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The Asymptotic Behaviour of Semigroups of Linear Operators

Jan van Neerven

Edit� par Springer, Basel, Birkh�user Basel, Birkh�user Jul 1996, 1996

ISBN 10 : 3764354550 ISBN 13 : 9783764354558

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Buch. Etat : Neu. This item is printed on demand - it takes 3-4 days longer - 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. 241 pp. Englisch. N� de r�f. du vendeur 9783764354558

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The Asymptotic Behaviour of Semigroups of Linear Operators (Operator Theory: Advances and Applications, 88)

Neerven, Jan Van

Edit� par Birkh�user, 1996

ISBN 10 : 3764354550 ISBN 13 : 9783764354558

Neuf Couverture rigide

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The Asymptotic Behaviour of Semigroups of Linear Operators

Jan Van Neerven

Edit� par Birkh�user Basel, 1996

ISBN 10 : 3764354550 ISBN 13 : 9783764354558

Neuf Couverture rigide

Vendeur : AHA-BUCH GmbH, Einbeck, Allemagne

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Buch. Etat : Neu. Druck auf Anfrage Neuware - Printed after ordering - 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. N� de r�f. du vendeur 9783764354558

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