On Riemann problems for monogenic functions in lower dimensional non-commutative Clifford algebras

TL;DR

This paper investigates Riemann boundary value problems for monogenic functions valued in lower-dimensional non-commutative Clifford algebras, providing explicit solutions and illustrative examples.

Contribution

It offers explicit solutions to Riemann problems in the context of monogenic functions within lower-dimensional non-commutative Clifford algebras, a novel approach in this area.

Findings

Explicit solutions to Riemann boundary value problems are derived.

Concrete examples demonstrate the applicability of the solutions.

The methods extend the understanding of monogenic functions in non-commutative Clifford algebras.

Abstract

In this paper, we mainly consider the Riemann boundary value problems for lower dimensional non-commutative Clifford algebras valued monogenic functions. The solutions are given in an explicit way and concrete examples are presented to illustrate the results.