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local convoluted semigroup

Proceedings of the Edinburgh Mathematical Society (1)

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THE HILLE–YOSIDA THEOREM FOR LOCAL CONVOLUTED SEMIGROUPS
Valentin Keyantuo, Claus Müller, Peter Vieten
Journal:

Proceedings of the Edinburgh Mathematical Society / Volume 46 / Issue 2 / June 2003

Published online by Cambridge University Press:

04 July 2003, pp. 395-413
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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