On Shilov boundary and Gelfand spectrum of algebras of generalized analytic functions

Abstract

Let $S$ be a discrete abelian semigroup with unit and concellations and $\hat{S}$ the semigroup of semicharacters of $S$. We shaw that the strong boundary and the Shilov boundary of the algebra of generalized analytic functions defined on $\hat{S}$ are unions of some maximal subgroups of $\hat{S}$. We shaw also that the both boundaries coincide with the character group of $S$ if $S$ does not contain nontrivial simple ideals. In the last case the Gelfand spectrum of the algebra under consideration is calculated.

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