Моногенні функції зі значеннями у комутативних комплексних алгебрах  другого рангу з одиницею та узагальнене бігармонічне рівняння з подвійною характеристикою

S. V. Gryshchuk

doi:10.37863/umzh.v74i1.6948

S. V. Gryshchuk Inst. Math. Acad. Sci. Ukraine, Kiev

DOI: https://doi.org/10.37863/umzh.v74i1.6948

Abstract

UDC 517.9

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

Abstract

References