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

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

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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Published
24.01.2022
How to Cite
Gryshchuk S. V. “Monogenic Functions With Values in Commutative Complex Algebras of the Second Rank With Unity and the Generalized Biharmonic Equation With Double Characteristics”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 74, no. 1, Jan. 2022, pp. 14 -23, doi:10.37863/umzh.v74i1.6948.
Section
Research articles