Monographs in Mathematics

Vector-valued Laplace Transforms and Cauchy Problems

Second Edition

Authors: Arendt, W., Batty, C.J.K., Hieber, M., Neubrander, F.

  • Standard reference on Laplace transforms
  • Includes the nontrivial applications of functional analysis
  • Accessible and self-contained text
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About this book

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

Reviews

From the reviews:

Written in a clear and accessible style and containing results obtained mainly in the last 15 years, the book is recommended to students and researchers in abstract evolution equations or interested in nontrivial applications of functional analysis.

Ştefan Cobzaş, Mathematica, Vol. 44.1 (2002)

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!

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

From the reviews of the second edition:

“This monograph is undoubtedly a valuable contribution to the abstract theory of Cauchy problems. … this book can serve as an excellent guide for the Laplace transform and Tauberian theorems in the Banach space setting. A special appreciation has to be given to the Notes which are included in each chapter … .” (Yakov Yakubov, Zentralblatt MATH, Vol. 1226, 2012)


Table of contents (8 chapters)

  • The Laplace Integral

    Arendt, Wolfgang (et al.)

    Pages 5-62

  • The Laplace Transform

    Arendt, Wolfgang (et al.)

    Pages 63-106

  • Cauchy Problems

    Arendt, Wolfgang (et al.)

    Pages 107-238

  • Asymptotics of Laplace Transforms

    Arendt, Wolfgang (et al.)

    Pages 243-335

  • Asymptotics of Solutions of Cauchy Problems

    Arendt, Wolfgang (et al.)

    Pages 337-395

Buy this book

eBook $109.00
price for USA (gross)
  • ISBN 978-3-0348-0087-7
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $149.00
price for USA
  • ISBN 978-3-0348-0086-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $149.00
price for USA
  • ISBN 978-3-0348-0327-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Vector-valued Laplace Transforms and Cauchy Problems
Book Subtitle
Second Edition
Authors
Series Title
Monographs in Mathematics
Series Volume
96
Copyright
2011
Publisher
Birkhäuser Basel
Copyright Holder
Birkhäuser Basel AG
eBook ISBN
978-3-0348-0087-7
DOI
10.1007/978-3-0348-0087-7
Hardcover ISBN
978-3-0348-0086-0
Softcover ISBN
978-3-0348-0327-4
Series ISSN
1017-0480
Edition Number
2
Number of Pages
XII, 540
Topics