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Symmetry
Volume 17
Issue 11
10.3390/sym17111974
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Article

Descriptions of Spectra of Algebras of Bounded-Type Block-Symmetric Analytic Functions

by
Viktoriia Kravtsiv
and
Andriy Zagorodnyuk
*
Faculty of Mathematics and Computer Science, Vasyl Stefanyk Carpathian National University, 57 Shevchenka Str., 76018 Ivano-Frankivsk, Ukraine
*
Author to whom correspondence should be addressed.
Symmetry 2025, 17(11), 1974; https://doi.org/10.3390/sym17111974
Submission received: 26 September 2025 / Revised: 29 October 2025 / Accepted: 13 November 2025 / Published: 15 November 2025
(This article belongs to the Special Issue Symmetry in Mathematical Analysis and Applications, 2nd Edition)
Versions Notes

Abstract

This paper is devoted to the study of the algebra of bounded-type block-symmetric analytic functions on the Banach space ℓ1(Cs). In particular, it presents a description of the spectrum of this algebra in terms of exceptional characters ϕα and characters that can be associated with exponential-type functions of several variables with plane zeros. Due to this representation, it is proven that every element of the spectrum is a convolution of an exceptional character with a point evaluation functional.
Keywords: block-symmetric polynomial; block-symmetric analytic function; spectrum of algebra; analytic functions of bounded type; entire functions with plane zeros block-symmetric polynomial; block-symmetric analytic function; spectrum of algebra; analytic functions of bounded type; entire functions with plane zeros

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MDPI and ACS Style

Kravtsiv, V.; Zagorodnyuk, A. Descriptions of Spectra of Algebras of Bounded-Type Block-Symmetric Analytic Functions. Symmetry 2025, 17, 1974. https://doi.org/10.3390/sym17111974

AMA Style

Kravtsiv V, Zagorodnyuk A. Descriptions of Spectra of Algebras of Bounded-Type Block-Symmetric Analytic Functions. Symmetry. 2025; 17(11):1974. https://doi.org/10.3390/sym17111974

Chicago/Turabian Style

Kravtsiv, Viktoriia, and Andriy Zagorodnyuk. 2025. "Descriptions of Spectra of Algebras of Bounded-Type Block-Symmetric Analytic Functions" Symmetry 17, no. 11: 1974. https://doi.org/10.3390/sym17111974

APA Style

Kravtsiv, V., & Zagorodnyuk, A. (2025). Descriptions of Spectra of Algebras of Bounded-Type Block-Symmetric Analytic Functions. Symmetry, 17(11), 1974. https://doi.org/10.3390/sym17111974

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