Geodesic
The Shilov boundary and the Gelfand spectrum of algebras of generalized analytic functions
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 3 (2011), pp. 41-49.

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Let $S$ be discrete abelian semigroup with unit and consellations. We show that the strong boundary and the Shilov boundary of the algebra of generalized analytic functions on the semigroup $\widehat S$ of semicharacters of $S$ are unions of some maximal subgroups of $\widehat S$. If $S$ does not contain nontrivial simple ideals, then both boundaries coincide with the character group of $S$. In this case, the Gelfand spectrum of the algebra under consideration has been calculated.
Keywords: Shilov boundary, Gelfand spectrum, uniform algebra, generalized analytic function. 
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A. R. Mirotin. The Shilov boundary and the Gelfand spectrum of algebras of generalized analytic functions. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 3 (2011), pp. 41-49. http://geodesic.mathdoc.fr/item/IVM_2011_3_a4/

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