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.
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Platonov, S.S. Spectral synthesis for the space of tempered solutions of a convolution system on discrete Abelian groups. Acta Math. Hungar. 157, 141–153 (2019). https://doi.org/10.1007/s10474-018-0873-0
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DOI: https://doi.org/10.1007/s10474-018-0873-0