Spectra of algebras of block-symmetric analytic functions of bounded type

A. Zagorodnyuk; V. V.  Kravtsiv

doi:10.30970/ms.58.1.69-81

A. Zagorodnyuk Vasyl Stefanyk Precarpathian National University Ivano-Frankivsk, Ukraine
V. V. Kravtsiv Vasyl Stefanyk Precarpathian National University Ivano-Frankivsk, Ukraine

DOI: https://doi.org/10.30970/ms.58.1.69-81

Keywords: block-symmetric polynomials;, block-symmetric analytic functions;, spectrum of algebras;, symmetric intertwining operators;, symmetric convolution

Abstract

We investigate algebras of block-symmetric analytic functions on spaces $\ell_{p}(\mathbb{C}^s)$ which are $\ell_{p}$-sums of $\mathbb{C}^{s}.$ We consider properties of algebraic bases of block-symmetric polynomials,
intertwining operations on spectra of the algebras and representations of the spectra as a semigroup of analytic functions of exponential type of several variables. All invertible elements of the semigroup are described for the case $p=1.$

Author Biographies

A. Zagorodnyuk, Vasyl Stefanyk Precarpathian National University Ivano-Frankivsk, Ukraine

Vasyl Stefanyk Precarpathian National University
Ivano-Frankivsk, Ukraine

V. V. Kravtsiv, Vasyl Stefanyk Precarpathian National University Ivano-Frankivsk, Ukraine

Vasyl Stefanyk Precarpathian National University
Ivano-Frankivsk, Ukraine

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