An analog of the Hille theorem for hypercomplex functions in a finite-dimensional commutative algebra
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| Název: | An analog of the Hille theorem for hypercomplex functions in a finite-dimensional commutative algebra |
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| Autoři: | Plaksa, S. A., Shpakivskyi, V. S., Tkachuk, M. V. |
| Zdroj: | Matematychni Studii. 64:32-41 |
| Publication Status: | Preprint |
| Informace o vydavateli: | Ivan Franko National University of Lviv, 2025. |
| Rok vydání: | 2025 |
| Témata: | Mathematics - Analysis of PDEs, Mathematics - Complex Variables, FOS: Mathematics, 13-11, Complex Variables (math.CV), Analysis of PDEs (math.AP) |
| Popis: | We prove that a locally bounded and differentiable in the sense of Gâteaux function given in a finite-dimensional commutative Banach algebra over the complex field is also differentiable in the sense of Lorc and it is a monogenic function. The algebra $\mathbb{A}_n^m$ has the Cartan basis for which the first $m$ basic vectors $I_1,$ $I_2,$ $\ldots,$ $I_m$ are idempotents, and next $n-m$ basis vectors $I_{m+1},I_{m+2},\dots,I_n$ are nilpotent elements.Every locally bounded and differentiable in the sense of Gâteaux function $\Phi\colon \Omega\rightarrow\mathbb{A}_n^m$ can be represented in the form of linear combination of these idempotents, nilpotents and corresponding Cauchy-type integrals. |
| Druh dokumentu: | Article |
| ISSN: | 2411-0620 1027-4634 |
| DOI: | 10.30970/ms.64.1.32-41 |
| DOI: | 10.48550/arxiv.2502.08809 |
| Přístupová URL adresa: | http://arxiv.org/abs/2502.08809 |
| Rights: | CC BY NC ND arXiv Non-Exclusive Distribution |
| Přístupové číslo: | edsair.doi.dedup.....53ec9b9d4fe447807598777f6eb87bf9 |
| Databáze: | OpenAIRE |
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Nájsť tento článok vo Web of Science | Abstrakt: | We prove that a locally bounded and differentiable in the sense of Gâteaux function given in a finite-dimensional commutative Banach algebra over the complex field is also differentiable in the sense of Lorc and it is a monogenic function. The algebra $\mathbb{A}_n^m$ has the Cartan basis for which the first $m$ basic vectors $I_1,$ $I_2,$ $\ldots,$ $I_m$ are idempotents, and next $n-m$ basis vectors $I_{m+1},I_{m+2},\dots,I_n$ are nilpotent elements.Every locally bounded and differentiable in the sense of Gâteaux function $\Phi\colon \Omega\rightarrow\mathbb{A}_n^m$ can be represented in the form of linear combination of these idempotents, nilpotents and corresponding Cauchy-type integrals. |
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| ISSN: | 24110620 10274634 |
| DOI: | 10.30970/ms.64.1.32-41 |