Monogenic functions with values in сommutative сomplex algebras of the second rank with unit and generalized biharmonic equation with simple nonzero simple characteristics

• Date: 2021
• Main Authors: Gryshchuk , S. V., Грищук, С. В.
• Format: Article
• Language: Ukrainian
• Published: Institute of Mathematics, NAS of Ukraine 2021
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/6199
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

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}_...