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Sharp extensions for convoluted solutions of wave equations

Authors
  • Miana, Pedro J.
  • Poblete, Verónica
Type
Preprint
Publication Date
Mar 29, 2013
Submission Date
Mar 29, 2013
Identifiers
arXiv ID: 1303.7346
Source
arXiv
License
Yellow
External links

Abstract

In this paper we give sharp extensions of convoluted solutions of wave equations in abstract Banach spaces. The main technique is to use the algebraic structure, for convolution products $\ast$ and $\ast_c$, of these solutions which are defined by a version of the Duhamel's formula. We define algebra homomorphisms, for the convolution product $\ast_c$, from a certain set of test-functions and apply our results to concrete examples of abstract wave equations.

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