Monogenic functions with values in сommutative сomplex algebras of the second rank with unit and generalized biharmonic equation with simple nonzero simple characteristics
УДК 517.5, 539.3 Among all two-dimensional algebras of the second rank with a unit $e$ over the field of complex numbers $\mathbb{C},$ we found a semisimple algebra $\mathbb{B}_{0}:=\{c_1 e+c_2\omega\colon c_k\in\mathbb{C},k=1,2\},$ $\omega^2=e,$ containing bases $\{e_1,e_2\}$ such that $\mathbb{B}_...
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| Datum: | 2021 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Ukrainisch |
| Veröffentlicht: |
Institute of Mathematics, NAS of Ukraine
2021
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/6199 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
| Завантажити файл: |  |
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Ukrains’kyi Matematychnyi Zhurnal| Zusammenfassung: | УДК 517.5, 539.3
Among all two-dimensional algebras of the second rank with a unit $e$ over the field of complex numbers $\mathbb{C},$ we found a semisimple algebra $\mathbb{B}_{0}:=\{c_1 e+c_2\omega\colon c_k\in\mathbb{C},k=1,2\},$ $\omega^2=e,$ containing bases $\{e_1,e_2\}$ such that $\mathbb{B}_{0}$-valued ``analytic'' functions $\Phi(xe_1+ye_2),$ where $x, y$ are real variables, satisfy a homogeneous partial differential equation of the fourth order that has only simple nonzero characteristics.The set of pairs $(\{e_1,e_2\},\Phi)$ is described in an explicit form. |
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| DOI: | 10.37863/umzh.v73i4.6199 |