a1 Department of Mathematics, University of Puerto Rico, Rio Piedras 00931, Puerto Rico (firstname.lastname@example.org)
a2 Fachbereich Mathematik der Universität Kaiserslautern, Erwin-Schrödinger Strasse, 67663 Kaiserslautern, Germany (email@example.com)
The characterization theorem for the Banach-space-valued local Laplace transform established by Keyantuo, Müller and Vieten is used to obtain a real variable characterization of generators of local convoluted semigroups. The concept of local convoluted semigroups extends that of distribution as well as ultradistribution semigroups. Complete characterizations existed only for exponentially bounded semigroups integrated $\alpha$ times, whereas for the non-exponential case generation results had been obtained in terms of complex conditions only.
AMS 2000 Mathematics subject classification: Primary 47D03; 47D06; 44A10
(Received March 16 2000)