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Israel Journal of Mathematics

, Volume 59, Issue 3, pp 327–352 | Cite as

Vector-valued laplace transforms and cauchy problems

  • Wolfgang Arendt
Article

Abstract

Linear differential equations in Banach spaces are systematically treated with the help of Laplace transforms. The central tool is an “integrated version” of Widder’s theorem (characterizing Laplace transforms of bounded functions). It holds in any Banach space (whereas the vector-valued version of Widder’s theorem itself holds if and only if the Banach space has the Radon-Nikodým property). The Hille-Yosida theorem and other generation theorems are immediate consequences. The method presented here can be applied to operators whose domains are not dense.

Keywords

Banach Space Cauchy Problem Uniqueness Theorem Linear Differential Equation Banach Lattice 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© The Weizmann Science Press of Israel 1987

Authors and Affiliations

  • Wolfgang Arendt
    • 1
  1. 1.Mathematisches Institut der UniversitätTübingenFRG

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