Vector-valued Laplace Transforms and Cauchy Problems Second Edition /

• Main Authors: Arendt, Wolfgang (Author), Batty, Charles J.K (Author), Hieber, Matthias (Author), Neubrander, Frank (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Basel : Springer Basel, 2011.
• Series: Monographs in Mathematics ; 96
• Subjects: Mathematics.; Partial differential equations.; Partial Differential Equations.

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...

Table of Contents:

• 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.