The hypercomplex analysis in both commutative and noncommutative algebras has been
developing very intensively over last few decades. Its applications are developed to …

We consider a commutative algebra over the field of complex numbers with a basis {e1, e2}
satisfying the conditions,. Let D be a bounded domain in the Cartesian plane xOy and …

The idea of an algebraic-analytic approach to equations of mathematical physics means to
find a commutative Banach algebra such that monogenic functions with values in this …

We develop a hypercomplex method of solving of boundary value problems for biharmonic
functions. This method is based on a relation between biharmonic functions and monogenic …

The methods involving the functions analytic in a complex plane for plane potential fields
inspire the search for the analogous efficient methods for solving the spatial and …

We consider a two-dimensional commutative algebra B over the field of complex numbers.
The algebra B is associated with the biharmonic equation. For monogenic functions with …

We establish integral theorems for monogenic functions taking values in an infinite-
dimensional commutative Banach algebra associated with spatial potential solenoid fields …

We develop a method for the reduction of the Dirichlet problem for the Stokes flow function in
a simply-connected domain of the meridian plane to the Cauchy singular integral equation …

This paper extends approach developed in a recent author's paper on analytic models of
potential fields in inhomogeneous media. New three-dimensional analytic models of …

We obtain integral representations of generalized axially symmetric potentials via analytic
functions of a complex variable that are defined in an arbitrary simply connected bounded …