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Abstract
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Abstract and Applied Analysis
Volume 2004 (2004), Issue 1, Pages 69-90
doi:10.1155/S1085337504309073

Laplace transform generation theorems and local Cauchy problems

Claus Müller

Fachbereich Mathematik, Universitaet Kaiserslautern, Erwin Schroedinger Strasse, Kaiserslautern 67655, Germany

Abstract

We give new criterions to decide if some vector-valued function is a local Laplace transform and apply this to the theory of local Cauchy problems. This leads to an improvement of known results and new Hille-Yosida-type theorems for local convoluted semigroups.