Vector-valued Laplace Transforms and Cauchy Problems: v. 96 (Monographs in Mathematics)

Wolfgang Arendt (Author), Charles J.K. Batty (Author), Frank Neubrander (Author)

ISBN 10: 3764365498 / ISBN 13: 9783764365493

Published by Springer Basel, 2001

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Bibliographic Details

• Title: Vector-valued Laplace Transforms and Cauchy Problems: v. 96 (Monographs in Mathematics)
• Publisher: Springer Basel
• Publication Date: 2001
• Language: English
• ISBN 10: 3764365498
• ISBN 13: 9783764365493
• Binding: Hardcover
• Edition: 1st Edition
• Condition: As New
• Seller catalogs:
  • Technical

About this title

Synopsis

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 second edition contains detailed notes on the developments in the last decade. They include, for instance, a new characterization of well-posedness of abstract wave equations in Hilbert space due to M. Crouzeix. Moreover new quantitative results on asymptotic behaviour of Laplace transforms have been added. The references are updated and some errors have been corrected.