Monogenic functions with values in commutative complex algebras of the second rank with unity and the generalized biharmonic equation with double characteristics
UDC 517.9We prove that any two-dimensional algebra $\mathbb{B}_{\ast}$ of the second rank with unity over the field of complex numbers $\mathbb{C}$ contains basises $\{e_1,e_2\},$ for which the $\mathbb{B}_{\ast}$-valued ``analytic'' functions $\Phi(xe_1+ye_2),$ where $x$ and $y$ a...
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| Date: | 2022 |
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| Main Authors: | , |
| Format: | Article |
| Language: | Ukrainian |
| Published: |
Institute of Mathematics, NAS of Ukraine
2022
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/6948 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
| Download file: |  |
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Ukrains’kyi Matematychnyi Zhurnal| Summary: | UDC 517.9We prove that any two-dimensional algebra $\mathbb{B}_{\ast}$ of the second rank with unity over the field of complex numbers $\mathbb{C}$ contains basises $\{e_1,e_2\},$ for which the $\mathbb{B}_{\ast}$-valued ``analytic'' functions $\Phi(xe_1+ye_2),$ where $x$ and $y$ are real variables, satisfy a homogeneous PDE of the fourth order with complex coefficients such that its characteristic equation has just one multiple root and the other roots are simple.The set of all triples $(\mathbb{B}_{\ast}, \{e_1,e_2\}, \Phi)$ is described in the explicit form. |
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| DOI: | 10.37863/umzh.v74i1.6948 |