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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| Date: | 2025 |
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| Main Authors: | , |
| Format: | Article |
| Language: | English |
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Lugansk National Taras Shevchenko University
2025
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| Online Access: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2352 |
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| Journal Title: | Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics| _version_ | 1856543031855939584 |
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| author | Gefter, Sergiy L. Piven', Aleksey L. |
| author_facet | Gefter, Sergiy L. Piven', Aleksey L. |
| author_sort | Gefter, Sergiy L. |
| baseUrl_str | |
| collection | OJS |
| datestamp_date | 2025-08-13T10:04:13Z |
| 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. |
| first_indexed | 2025-12-02T15:39:48Z |
| format | Article |
| id | admjournalluguniveduua-article-2352 |
| institution | Algebra and Discrete Mathematics |
| language | English |
| last_indexed | 2025-12-02T15:39:48Z |
| publishDate | 2025 |
| publisher | Lugansk National Taras Shevchenko University |
| record_format | ojs |
| 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 |
| 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 |
| title | 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_short | Formal functional calculus for copolynomials over a commutative ring |
| title_sort | formal functional calculus for copolynomials over a commutative ring |
| topic | copolynomial \(\delta\)-function formal power series multiplication of copolynomials formal functional calculus 13B25 46H30 13J05 |
| topic_facet | copolynomial \(\delta\)-function formal power series multiplication of copolynomials formal functional calculus 13B25 46H30 13J05 |
| url | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2352 |
| work_keys_str_mv | AT geftersergiyl formalfunctionalcalculusforcopolynomialsoveracommutativering AT pivenalekseyl formalfunctionalcalculusforcopolynomialsoveracommutativering |