Formal functional calculus for copolynomials over a commutative ring

We study the copolynomials, i.e. \(K\)-linear mappings from the ring of polynomials \(K[x_1,...,x_n]\) into the commutative ring \(K\). With the help of the Cauchy-Stieltjes transform of a copolynomial we introduce and study a multiplication of copolynomials. We build a counterpart of formal functio...

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Datum:2025
Hauptverfasser: Gefter, Sergiy L., Piven', Aleksey L.
Format: Artikel
Sprache:English
Veröffentlicht: Lugansk National Taras Shevchenko University 2025
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Online Zugang:https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2352
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Algebra and Discrete Mathematics
id admjournalluguniveduua-article-2352
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spelling admjournalluguniveduua-article-23522025-08-13T10:04:13Z Formal functional calculus for copolynomials over a commutative ring Gefter, Sergiy L. Piven', Aleksey L. copolynomial, \(\delta\)-function, formal power series, multiplication of copolynomials, formal functional calculus 13B25, 46H30, 13J05 We study the copolynomials, i.e. \(K\)-linear mappings from the ring of polynomials \(K[x_1,...,x_n]\) into the commutative ring \(K\). With the help of the Cauchy-Stieltjes transform of a copolynomial we introduce and study a multiplication of copolynomials. We build a counterpart of formal functional calculus for the case of a finite number of copolynomials. We obtain an analogue of the spectral mapping theorem and analogues of the Taylor formula and the Riesz-Dunford formula. Lugansk National Taras Shevchenko University 2025-08-13 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2352 10.12958/adm2352 Algebra and Discrete Mathematics; Vol 39, No 2 (2025) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2352/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/2352/1279 Copyright (c) 2025 Algebra and Discrete Mathematics
institution Algebra and Discrete Mathematics
baseUrl_str
datestamp_date 2025-08-13T10:04:13Z
collection OJS
language English
topic copolynomial
\(\delta\)-function
formal power series
multiplication of copolynomials
formal functional calculus
13B25
46H30
13J05
spellingShingle copolynomial
\(\delta\)-function
formal power series
multiplication of copolynomials
formal functional calculus
13B25
46H30
13J05
Gefter, Sergiy L.
Piven', Aleksey L.
Formal functional calculus for copolynomials over a commutative ring
topic_facet copolynomial
\(\delta\)-function
formal power series
multiplication of copolynomials
formal functional calculus
13B25
46H30
13J05
format Article
author Gefter, Sergiy L.
Piven', Aleksey L.
author_facet Gefter, Sergiy L.
Piven', Aleksey L.
author_sort Gefter, Sergiy L.
title Formal functional calculus for copolynomials over a commutative ring
title_short Formal functional calculus for copolynomials over a commutative ring
title_full Formal functional calculus for copolynomials over a commutative ring
title_fullStr Formal functional calculus for copolynomials over a commutative ring
title_full_unstemmed Formal functional calculus for copolynomials over a commutative ring
title_sort formal functional calculus for copolynomials over a commutative ring
description We study the copolynomials, i.e. \(K\)-linear mappings from the ring of polynomials \(K[x_1,...,x_n]\) into the commutative ring \(K\). With the help of the Cauchy-Stieltjes transform of a copolynomial we introduce and study a multiplication of copolynomials. We build a counterpart of formal functional calculus for the case of a finite number of copolynomials. We obtain an analogue of the spectral mapping theorem and analogues of the Taylor formula and the Riesz-Dunford formula.
publisher Lugansk National Taras Shevchenko University
publishDate 2025
url https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2352
work_keys_str_mv AT geftersergiyl formalfunctionalcalculusforcopolynomialsoveracommutativering
AT pivenalekseyl formalfunctionalcalculusforcopolynomialsoveracommutativering
first_indexed 2025-12-02T15:39:48Z
last_indexed 2025-12-02T15:39:48Z
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