Vector-Valued Laplace Transforms and Cauchy Problems

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.

Vector-Valued Laplace Transforms and Cauchy Problems features in the following genres: Differential calculus and equations

Vector-Valued Laplace Transforms and Cauchy Problems is available in Paperback

Vector-Valued Laplace Transforms and Cauchy Problems was written by Wolfgang Arendt, Charles JK Batty, Matthias Hieber, Frank Neubrander and published by Birkhauser an imprint of Springer Basel

Vector-Valued Laplace Transforms and Cauchy Problems has 540 pages

Yes it is part of Monographs in Mathematics series