Spectral synthesis for the space of tempered solutions of a convolution system on discrete Abelian groups

Abstract

We consider a problem of spectral synthesis in the topological vector space $${\mathcal{M}(G)}$$ of tempered functions on a discrete Abelian group G. It is proved that the space of tempered solutions of a convolution system on discrete Abelian groups admits spectral synthesis, that is the space of tempered solutions of a convolution system coincides with the closed linear span in $${\mathcal{M}(G)}$$ of all exponential monomial solutions of this system.