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Algebras of free holomorphic functions and localizations
Sbornik. Mathematics, Tome 210 (2019) no. 9, pp. 1288-1304 Cet article a éte moissonné depuis la source Math-Net.Ru

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We consider the algebras of holomorphic functions on a free polydisc $\mathscr F^T(\mathbb D_R^n)$, $\mathscr F(\mathbb D_R^n)$ and the algebra of holomorphic functions on a free ball $\mathscr F(\mathbb B_r^n)$. We show that the algebra $\mathscr F(\mathbb D_R^n)$ is a localization of a free algebra and, moreover, is a free analytic algebra with $n$ generators (in the sense of J. Taylor), while the algebra $\mathscr F(\mathbb B_r^n)$ is not a localization of a free algebra. In addition we prove that the class of localizations of free algebras and the class of free analytic algebras are closed under the operation of the Arens-Michael free product. Bibliography: 21 titles.
Keywords: localization, free analytic algebra, Arens-Michael free product, algebra of holomorphic functions on a free polydisc, algebra of holomorphic functions on a free ball. 
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     title = {Algebras of free holomorphic functions and localizations},
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K. A. Syrtseva. Algebras of free holomorphic functions and localizations. Sbornik. Mathematics, Tome 210 (2019) no. 9, pp. 1288-1304. http://geodesic.mathdoc.fr/item/SM_2019_210_9_a3/

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