Asymptotic behaviour semigroups linear (9 Ergebnisse)
Verlag: Basel, Birkhäuser, , 1996
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XII/236 S./pp., Originalpappband (publisher's cardboard covers), Bibliotheksexemplar in sehr gutem Zustand / exlibrary in excellent condition (Stempel auf Titel / title stamped, Rückenschildchen / lettering pannel to the spine, Block sehr gut / contents fine, keine Unterstreichungen oder Anstreichungen / no underlining or remark…s, nicht in Folie eingeschlagen / not wrapped up in foil), (Operator Theory Advances and Applications 88), Sprache: englisch.
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Paperback. Zustand: Brand New. reprint edition. 256 pages. 9.25x6.10x0.58 inches. In Stock.
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Taschenbuch. Zustand: 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.
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Buch. Zustand: 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 maturi…ty. 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.
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Zustand: Sehr gut. Zustand: Sehr gut | Seiten: 256 | Sprache: Englisch | Produktart: Bücher | 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 cer…tain 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.
