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arXiv · 1303.6944

Sharp extensions for convoluted solutions of abstract Cauchy problems

Valentin Keyantuo·Pedro J. Miana·Luis Sánchez-Lajusticia
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Abstract

In this paper we give sharp extension results for convoluted solutions of abstract Cauchy problems in Banach spaces. The main technique is the use of algebraic structure (for usual convolution product $\ast$) of these solutions which are defined by a version of the Duhamel formula. We define algebra homomorphisms from a new class of test-functions and apply our results to concrete operators. Finally, we introduce the notion of $k$-distribution semigroups to extend previous concepts of distribution semigroups.

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Valentin Keyantuo, Pedro J. Miana, Luis Sánchez-Lajusticia. 2013-03-27. Sharp extensions for convoluted solutions of abstract Cauchy problems. https://arxiv.org/abs/1303.6944

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