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- ДокументMonogenic functions and harmonic vectors(2023) Sergiy PlaksaWe consider special topological vector spaces with a commutative multiplication for some of elements of the spaces and monogenic functions taking values in these spaces.Monogenic functions are understood as continuous and differentiable in the sense of G^ateaux functions.We describe relations between the mentioned monogenic functions and harmonic vectors in the three-dimensional real space and establish sufficient conditions for infinite monogeneity of functions. Unlike the classical complex analysis, it is done in the case where the validity of the Cauchy integral formula for monogenic functions remains an open problem.
- Документσ-monogenic functions in commutative algebras(2023) Vitalii ShpakivskyiIn finite-dimensional commutative associative algebra, the concept of σ-monogenic function is introduced. Necessary and sufficient conditions for σ-monogeneity have been established. In some low-dimensional algebras, with a special choice of σ, the representation of σ-monogenic functions is obtained using holomorphic functions of a complex variable. We proposed the application of σ-monogenic functions with values in two-dimensional biharmonic algebra to representation of solutions of two-dimensional biharmonic equation.
- ДокументA.K. Bakhtin. Scientific legacy(2023) Iryna Denega, Yaroslav ZabolotnyiIn the paper we give a brief overview of the O. Bakhtin' scientific results