You might also like

More about Asymptotic Behaviour of Semigroups of Linear Operators

• Book details
• Synopsis
• Trending among others

You get 290 loyalty points

Book synopsis

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.

Book details

Book category Books in English Mathematics & science Mathematics Calculus & mathematical analysis

• Full title: Asymptotic Behaviour of Semigroups of Linear Operators
• Author: Jan van Neerven
• Language: English
• Binding: Hardback
• Number of pages: 241
• EAN: 9783764354558
• ISBN: 3764354550
• ID: 05289167
• Publisher: Birkhauser Verlag AG
• Weight: 1200 g
• Dimensions: 235 × 155 × 18 mm
• Date of publishing: 01. July 1996

Trending among others

---

---

---