Representation of spectra of algebras of block-symmetric analytic functions of bounded type

Kravtsiv, V. V.; Zagorodnyuk, Andriy

doi:10.15330/cmp.8.2.263-271

Cited by 8 publications

(11 citation statements)

References 6 publications

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“…General algebraic properties of block-symmetric polynomials of finite number of variables can be found in [12]. Algebras generated by block-symmetric polynomials on ℓ 1 and their spectra were investigated in [13], [14], [15].…”

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confidence: 99%

Note on separately symmetric polynomials on the Cartesian product of l1

Jawad¹

2018

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In the paper, we describe algebraic bases in algebras of separately symmetric polynomials which are defined on Cartesian products of n copies of ℓ 1. Also, we describe spectra of algebras of entire functions, generated by these polynomials as Cartesian products of spectra of algebras of symmetric analytic functions of bounded type on ℓ 1. Finally, we consider algebras of separately symmetric analytic functions of bounded type on infinite direct sums of copies of ℓ 1. In particular, we show that there is a homomorphism from such algebra onto the algebra of all analytic functions of bounded type on a Banach space X with an unconditional basis.

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confidence: 99%

Note on separately symmetric polynomials on the Cartesian product of l1

Jawad¹

2018

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“…Some generalizations of the Newton formulas for algebraic bases of block-symmetric polynomials were obtained in [18]. Spectra of algebras of block-symmetric polynomials and holomorphic functions and algebraic structures on the spectra were considered in [19,20]. Zeros of block-symmetric polynomials were investigated in [21].…”

Section: Introductionmentioning

confidence: 99%

Block-Supersymmetric Polynomials on Spaces of Absolutely Convergent Series

Kravtsiv

2024

Symmetry

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In this paper, we consider a supersymmetric version of block-symmetric polynomials on a Banach space of two-sided absolutely summing series of vectors in Cs for some positive integer s>1. We describe some sequences of generators of the algebra of block-supersymmetric polynomials and algebraic relations between the generators for the finite-dimensional case and construct algebraic bases of block-supersymmetric polynomials in the infinite-dimensional case. Furthermore, we propose some consequences for algebras of block-supersymmetric analytic functions of bounded type and their spectra. Finally, we consider some special derivatives in algebras of block-symmetric and block-supersymmetric analytic functions and find related Appell-type sequences of polynomials.

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“…Note that such kinds of algebras are much more complicated and in the general case have no algebraic basis (see e.g. [21,22,[24][25][26]37]). Note that if dim X < ∞, then block-symmetric polynomials are investigated in the classical theory of invariants and combinatorics [18,32,36].…”

Section: Introductionmentioning

confidence: 99%

“…This research is a continuation of investigations in [8][9][10] for symmetric analytic functions. Also, some presented results were obtained in [26] for block-symmetric analytic functions for a partial case of two-dimensional blocks. In Section 2, we consider properties of block-symmetric polynomials and algebraic bases of block-symmetric polynomials.…”

Section: Introductionmentioning

confidence: 99%

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

Zagorodnyuk

Kravtsiv

2022

Mat. Stud.

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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 $p=1.$

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Representation of spectra of algebras of block-symmetric analytic functions of bounded type

Cited by 8 publications

References 6 publications

Note on separately symmetric polynomials on the Cartesian product of l1

Note on separately symmetric polynomials on the Cartesian product of l1

Block-Supersymmetric Polynomials on Spaces of Absolutely Convergent Series

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

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