The Asymptotic Behaviour of Semigroups of Linear Operators

✍ Scribed by Jan van Neerven (auth.)

• Publisher: Birkhäuser Basel
• Year: 1996
• Tongue: English
• Leaves: 243
• Series: Operator Theory: Advances and Applications 88
• Edition: 1
• Category: Library

✦ Synopsis

This book presents a systematic account of the theory of asymptotic behaviour of semigroups of linear operators acting in a Banach space. The focus is on the relationship between asymptotic behaviour of the semigroup and spectral properties of its infinitesimal generator. The most recent developments in the field are included, such as the Arendt-Batty-Lyubich-Vu theorem, the spectral mapp- ing theorem of Latushkin and Montgomery-Smith, Weis's theorem on stability of positive semigroup in Lp-spaces, the stability theorem for semigroups whose resolvent is bounded in a half-plane, and a systematic theory of individual stability. Addressed to researchers and graduate students with interest in the fields of operator semigroups and evolution equations, this book is self-contained and provides complete proofs.

✦ Table of Contents

Front Matter....Pages i-xii
Spectral bound and growth bound....Pages 1-24
Spectral mapping theorems....Pages 25-71
Uniform exponential stability....Pages 73-111
Boundedness of the resolvent....Pages 113-147
Countability of the unitary spectrum....Pages 149-213
Back Matter....Pages 215-241

✦ Subjects

Operator Theory; Functional Analysis