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Vector-valued Laplace Transforms and Cauchy Problems

Vector-valued Laplace Transforms and Cauchy Problems
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Field name Details
Dewey Class 515.353 (DDC 23)
Title Vector-valued Laplace Transforms and Cauchy Problems ([Ebook]) / by Wolfgang Arendt, Charles J.K. Batty, Matthias Hieber, Frank Neubrander.
Author Arendt, Wolfgang
Added Personal Name Batty, Charles J.K.
Hieber, Matthias
Neubrander, Frank
Other name(s) SpringerLink (Online service)
Edition statement Second edition
Publication Basel : Birkhäuser , 2011.
Physical Details XII, 540 pages : online resource.
Series Monographs in mathematics ; 96
ISBN 9783034800877
Summary Note 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:
Contents note Preface to the First Edition -- Preface to the Second Edition -- I Laplace Transforms and Well-Posedness of Cauchy Problems -- 1 The Laplace Integral -- 2 The Laplace Transform -- 3 Cauchy Problems -- II Tauberian Theorems and Cauchy Problems -- 4 Asymptotics of Laplace Transforms -- 5 Asymptotics of Solutions of Cauchy Problems -- III Applications and Examples -- 6 The Heat Equation -- 7 The Wave Equation -- 8 Translation Invariant Operators on Lp(Rn) -- A Vector-valued Holomorphic Functions -- B Closed Operators -- C Ordered Banach Spaces -- D Banach Spaces which Contain c0 -- E Distributions and Fourier Multipliers -- Bibliography -- Notation -- Index.
System details note Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site http://dx.doi.org/10.1007/978-3-0348-0087-7
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