1996, ISBN: 9783764354558

Gebundene Ausgabe

Buch, Hardcover, 1996, Over the past ten years, the asymptotic theory of one-parameter semigroups of operators has witnessed an explosive development. A number oflong-standing open proble… Mehr…

Buch, Hardcover, 1996, 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. [PU: Springer Basel], Seiten: 241, Springer Basel, 1996<

1996, ISBN: 9783764354558

Gebundene Ausgabe

[ED: Gebunden], [PU: Birkhaeuser Basel], 1. Spectral bound and growth bound.- 1.1. C0—semigroups and the abstract Cauchy problem.- 1.2. The spectral bound and growth bound of a semi… Mehr…

[ED: Gebunden], [PU: Birkhaeuser Basel], 1. Spectral bound and growth bound.- 1.1. C0—semigroups and the abstract Cauchy problem.- 1.2. The spectral bound and growth bound of a semigroup.- 1.3. The, DE, [SC: 0.00], Neuware, gewerbliches Angebot, Hardcover, 241, [GW: 540g], 1. Auflage, Banküberweisung, PayPal, [CT: Naturwissenschaft/Mathematik / Sonstiges - Naturwissenschaften]<

ISBN: 9783764354558

Hardback. New. Presents an account of the theory of asymptotic behaviour of semigroups of linear operators acting in a Banach space. This work focuses on the relationship between asympto… Mehr…

Hardback. New. Presents an account of the theory of asymptotic behaviour of semigroups of linear operators acting in a Banach space. This work focuses on the relationship between asymptotic behaviour of the semigroup and spectral properties of its infinitesimal generator., 6<

1996, ISBN: 3764354550

[EAN: 9783764354558], Neubuch, [PU: Springer], pp. 260, Books