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 |
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| Sprache: | English |
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Lugansk National Taras Shevchenko University
2025
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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 |
| _version_ |
1850412151940841472 |