Jan van Neerven The Asymptotic Behaviour of Semigroups of Linear Operators 9783034899444

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Автор: Jan van Neerven
Название: The Asymptotic Behaviour of Semigroups of Linear Operators
ISBN: 9783034899444
Издательство: Springer
Классификация:

Функциональный анализ и преобразования

ISBN-10: 3034899440
Обложка/Формат: Paperback
Страницы: 241
Вес: 0.37 кг.
Дата издания: 01.10.2011
Серия: Operator Theory: Advances and Applications
Язык: English
Размер: 234 x 156 x 14
Основная тема: Mathematics
Ссылка на Издательство: Link
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Поставляется из: Германии
Описание: 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 Gelfands 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 Lyapunovs 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, Lyapunovs 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.

The Asymptotic Behaviour of Semigroups of Linear Operators, Jan van Neerven