arXiv subjects

Anatoliy A. Pogorui

Publications and source records attributed to Anatoliy A. Pogorui.

2 recordsLinked to original sources

arXiv2008

Solution of Partial Differential Equations by Method of Hyperholomorphic functions

It is well known that the real and imaginary parts of any holomorphic function are harmonic functions of two variables. In this paper we generalize this property to finite-dimensional commutative algebras. We prove that if some basis of a subspace of a commutative algebra satisfies a polynomial equation then components of a hyperholomorphic function on the subspace are solutions of the respective partial differential equation.

math.AP↗

arXiv2006

Hyperholomorphic functions on commutative algebras

In this paper we study properties of hyperholomorphic functions on commutative finite algebras. It is investigated the Cauchy-Riemann type conditions for hyperholomorphic functions. We prove that a hyperholomorphic function on a commutative finite algebra can be expanded in a Taylor series. We also present a technique for computing zeros of polynomials in some commutative algebras.

math.CV↗