Abstract and Applied Analysis
Volume 2004 (2004), Issue 1, Pages 69-90

Laplace transform generation theorems and local Cauchy problems

Claus Müller

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

Received 30 April 2001

Copyright © 2004 Claus Müller. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.