Vector-valued Laplace transforms and Cauchy problems
著者
書誌事項
Vector-valued Laplace transforms and Cauchy problems
（Monographs in mathematics, v. 96）
Birkhäuser Verlag, c2001
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注記
Includes bibliographical references (p. [487]-510) and index
内容説明・目次
内容説明
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.
目次
- Part 1 Laplace transforms and well-posedness of Cauchy problems: the Laplace integral
- the Laplace transform
- Cauchy problems. Part 2 Tauberian theorems and Cauchy problems: asymptotics of Laplace transforms
- asymptotics of solutions of Cauchy problems. Part 3 Applications and examples: the heat equation
- the wave equation
- translation invariant operators on "Lp(Rn)"
- appendices.
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