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SMOOTH SOLUTIONS OF VOLTERRA EQUATIONS VIA SEMIGROUPS

Part of: Groups and semigroups of linear operators, their generalizations and applications

Published online by Cambridge University Press:  01 October 2008

TOMÁŠ BÁRTA
TOMÁŠ BÁRTA*
Affiliation:
Faculty of Mathematics and Physics, Department of Mathematical Analysis, Charles University, Prague, Sokolovska 83,180 00 Prague 8, Czech Republic (email: barta@karlin.mff.cuni.cz)
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Abstract

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In this paper we introduce a class of left shift semigroups that are differentiable. With the help of perturbation theory for differentiable semigroups we show that solutions of an integrodifferential equation can be infinitely differentiable if the convolution kernel is sufficiently smooth and regular.

Keywords

differentiable semigroupbounded perturbationshift semigroupintegro-differential equation

MSC classification

Secondary: 47D06: One-parameter semigroups and linear evolution equations
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 78 , Issue 2 , October 2008 , pp. 249 - 260
Copyright
Copyright © 2008 Australian Mathematical Society

References

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