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Vector-valued Laplace Transforms and Cauchy Problems

Second Edition

  • Wolfgang Arendt
  • Charles J.K. Batty
  • Matthias Hieber
  • Frank Neubrander

Part of the Monographs in Mathematics book series (MMA, volume 96)

Table of contents

  1. Front Matter
    Pages i-xii
  2. Laplace Transforms and Well-Posedness of Cauchy Problems

    1. Front Matter
      Pages 1-4
    2. Wolfgang Arendt, Charles J. K. Batty, Matthias Hieber, Frank Neubrander
      Pages 5-62
    3. Wolfgang Arendt, Charles J. K. Batty, Matthias Hieber, Frank Neubrander
      Pages 63-106
    4. Wolfgang Arendt, Charles J. K. Batty, Matthias Hieber, Frank Neubrander
      Pages 107-238
  3. Tauberian Theorems and Cauchy Problems

    1. Front Matter
      Pages 239-242
    2. Wolfgang Arendt, Charles J. K. Batty, Matthias Hieber, Frank Neubrander
      Pages 243-335
    3. Wolfgang Arendt, Charles J. K. Batty, Matthias Hieber, Frank Neubrander
      Pages 337-395
  4. Applications and Examples

    1. Front Matter
      Pages 397-399
    2. Wolfgang Arendt, Charles J. K. Batty, Matthias Hieber, Frank Neubrander
      Pages 401-416
    3. Wolfgang Arendt, Charles J. K. Batty, Matthias Hieber, Frank Neubrander
      Pages 417-428
    4. Wolfgang Arendt, Charles J. K. Batty, Matthias Hieber, Frank Neubrander
      Pages 429-459
  5. Back Matter
    Pages 461-539

About this book

Introduction

This monograph gives a systematic account of the theory of vector-valued Laplace transforms, ranging from representation theory to Tauberian theorems. In parallel, the theory of linear Cauchy problems and semigroups of operators is developed completely in the spirit of Laplace transforms. Existence and uniqueness, regularity, approximation and above all asymptotic behaviour of solutions are studied. Diverse applications to partial differential equations are given. The book contains an introduction to the Bochner integral and several appendices on background material. It is addressed to students and researchers interested in evolution equations, Laplace and Fourier transforms, and functional analysis.

The authors have succeeded admirably in bringing together a wealth of recent material, much of which appears in book form for the first time. This authoritative work is likely to become a standard reference on both the Laplace transform and its applications to the abstract Cauchy problem. …

The book is an excellent textbook as well. Proofs are always transparent and complete, and many topics that could have been considered as background material are covered as well. All this makes the text very accessible and self-contained. Applications to concrete differential operators are given throughout the text. Each chapter ends with historical and bibliographical comments. … In summary, this book will be of interest to a wide audience of (functional) analysts and it should have a place in every mathematics library. Warmly recommended!

Jan van Neerven, Nieuw Archief voor Wiskunde, No. 3, 2003

Keywords

Evolution equations Laplace and Fourier transforms functional analysis

Authors and affiliations

  • Wolfgang Arendt
    • 1
  • Charles J.K. Batty
    • 2
  • Matthias Hieber
    • 3
  • Frank Neubrander
    • 4
  1. 1.Abt. Mathematik VUniversität UlmUlmGermany
  2. 2.St. John's CollegeUniversity of OxfordOxfordUnited Kingdom
  3. 3., Fachbereich MathematikTU DarmstadtDarmstadtGermany
  4. 4.Department of MathematicsLouisiana State UniversityBaton RougeUSA

Bibliographic information