Monogenic functions in finite-dimensional commutative associative algebras
Let $\mathbb{A}_n^m$ be an arbitrary $n$-dimensional commutative associative algebra overthe field of complex numbers with $m$ idempotents. Let $e_1=1$,\break $e_2,\ldots,e_k$, $2\leqk\leq 2n$, are linearly independent over the field of real numbers elements of $\mathbb{A}_n^m$.We consider monogenic...
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| Datum: | 2015 |
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| Ключові слова: | keywords |
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| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2015
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| Online Zugang: | https://trim.imath.kiev.ua/index.php/trim/article/view/176 |
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| Назва журналу: | Transactions of Institute of Mathematics of NAS of Ukraine |
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Transactions of Institute of Mathematics of NAS of Ukraine| Zusammenfassung: | Let $\mathbb{A}_n^m$ be an arbitrary $n$-dimensional commutative associative algebra overthe field of complex numbers with $m$ idempotents. Let $e_1=1$,\break $e_2,\ldots,e_k$, $2\leqk\leq 2n$, are linearly independent over the field of real numbers elements of $\mathbb{A}_n^m$.We consider monogenic (i.~e., continuous and differentiable in the sense of Gateaux) functions ofthe variable $\sum_{j=1}^k x_j\,e_j$\,, where $x_1,x_2,\ldots,x_k$ are real, and obtain aconstructive description of all mentioned functions by means of holomorphic functions of complexvariables. Due to this description obtain, that monogenic functions have Gateaux derivatives ofall orders. The present article is a generalization of the author's paper \cite{Shpakivskyi-2014},where mentioned results are obtained for $k=3$. |
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