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. 
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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