Monogenic functions with values in commutative complex algebras of the second rank with unity and the generalized biharmonic equation with double characteristics

• Date: 2022
• Main Authors: Gryshchuk , S. V., Грищук, С. В.
• Format: Article
• Language: Ukrainian
• Published: Institute of Mathematics, NAS of Ukraine 2022
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/6948
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

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...