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Vector-valued Laplace Transforms and Cauchy Problems
Second Edition
Langbeschreibung
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.
Inhaltsverzeichnis
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.
ISBN-13:
9783034800877
Veröffentl:
2011
Seiten:
540
Autor:
Wolfgang Arendt
Serie:
96, Monographs in Mathematics
eBook Typ:
PDF
eBook Format:
EPUB
Kopierschutz:
1 - PDF Watermark
Sprache:
Englisch
139,09 €*
Lieferzeit: Sofort lieferbar
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