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FINITE AND LOCAL LAPLACE TRANSFORMS IN BANACH SPACES

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 ([email protected])
Claus Müller
Affiliation:
Fachbereich Mathematik der Universität Kaiserslautern, Erwin-Schrödinger Strasse, 67663 Kaiserslautern, Germany ([email protected])
Peter Vieten
Affiliation:
Fachbereich Mathematik der Universität Kaiserslautern, Erwin-Schrödinger Strasse, 67663 Kaiserslautern, Germany ([email protected])
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Abstract

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We establish two characterizations of local Laplace transforms in Banach spaces. The first result follows the classic approach of Widder, while the second is in terms of vector-valued moment sequences. As a consequence, we derive characterizations of nilpotent semigroups.

AMS 2000 Mathematics subject classification: Primary 44A10; 47D03

Keywords

local Laplace transformfinite Laplace transformnilpotent semigroupmoment sequence
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 46 , Issue 2 , June 2003 , pp. 357 - 372
Copyright
Copyright © Edinburgh Mathematical Society 2003