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THE HILLE–YOSIDA THEOREM FOR LOCAL CONVOLUTED SEMIGROUPS

Published online by Cambridge University Press:  04 July 2003

Valentin Keyantuo ,
Claus Müller  and
Peter Vieten
Valentin Keyantuo
Affiliation:
Department of Mathematics, University of Puerto Rico, Rio Piedras 00931, Puerto Rico (keyantuo@upracd.upr.clu.edu)
Claus Müller
Affiliation:
Fachbereich Mathematik der Universität Kaiserslautern, Erwin-Schrödinger Strasse, 67663 Kaiserslautern, Germany (claus_mueller@mathematik.uni-kl.de)
Peter Vieten
Affiliation:
Fachbereich Mathematik der Universität Kaiserslautern, Erwin-Schrödinger Strasse, 67663 Kaiserslautern, Germany (claus_mueller@mathematik.uni-kl.de)
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Abstract

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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

Keywords

local Laplace transformlocal convoluted semigroupintegrated semigroupdistribution semigroupultradistribution semigroup.
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 46 , Issue 2 , June 2003 , pp. 395 - 413
Copyright
Copyright © Edinburgh Mathematical Society 2003