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.
"Sharp extensions for convoluted solutions of wave equations." Differential Integral Equations 28 (3/4) 309 - 332, March/April 2015.