On differentiable and monogenic functions in a harmonic algebra
For locally bounded and differentiable in the sense of G\^ateaux functions $\Phi$ given in a three-dimensional commutativeharmonic algebra with two-dimensional radical, we prove the following statement: if the function $\Phi$ domain is convex "in the radical direction" and the diff...
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| Datum: | 2017 |
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| Ключові слова: | keywords |
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| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
Інститут математики НАН України
2017
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| Online Zugang: | https://trim.imath.kiev.ua/index.php/trim/article/view/114 |
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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: | For locally bounded and differentiable in the sense of G\^ateaux functions $\Phi$ given in a three-dimensional commutativeharmonic algebra with two-dimensional radical, we prove the following statement: if the function $\Phi$ domain is convex "in the radical direction" and the difference $\zeta_1-\zeta_2$ belongs to the radical, the difference $\Phi(\zeta_1)-\Phi(\zeta_2)$ belongs also to the radical. As a result, we prove that locally bounded and differentiable in the sense of G\^ateaux functions are also differentiable in the sense of Lorch. |
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