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. 
@article{IVM_2011_3_a4,
     author = {A. R. Mirotin},
     title = {The {Shilov} boundary and the {Gelfand} spectrum of algebras of generalized analytic functions},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {41--49},
     publisher = {mathdoc},
     number = {3},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2011_3_a4/}
}
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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/