Udvidet returret til d. 31. januar 2025

Asymptotic Behaviour of Semigroups of Linear Operators

Bag om Asymptotic Behaviour of Semigroups of Linear Operators

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.

Vis mere
  • Sprog:
  • Engelsk
  • ISBN:
  • 9783034899444
  • Indbinding:
  • Paperback
  • Sideantal:
  • 241
  • Udgivet:
  • 1. oktober 2011
  • Udgave:
  • 11996
  • Størrelse:
  • 234x156x13 mm.
  • Vægt:
  • 394 g.
  • BLACK NOVEMBER
  Gratis fragt
Leveringstid: 8-11 hverdage
Forventet levering: 5. december 2024

Beskrivelse af Asymptotic Behaviour of Semigroups of Linear Operators

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.

Brugerbedømmelser af Asymptotic Behaviour of Semigroups of Linear Operators



Find lignende bøger
Bogen Asymptotic Behaviour of Semigroups of Linear Operators findes i følgende kategorier:

Gør som tusindvis af andre bogelskere

Tilmeld dig nyhedsbrevet og få gode tilbud og inspiration til din næste læsning.