A Riemann Boundary Value Problem in a Two-Dimensional Commutative Associative Banach Algebra

TL;DR

This paper investigates a Riemann boundary value problem for monogenic functions within a two-dimensional commutative associative Banach algebra, providing existence theorems and explicit solutions under various conditions.

Contribution

It introduces new existence results and explicit formulas for solutions to Riemann boundary value problems in a specific algebraic setting.

Findings

Existence theorems established for solutions under different assumptions.

Explicit formula derived for the solutions.

Conditions on coefficients and free terms identified.

Abstract

We consider a Riemann boundary value problem for monogenic functions in a two-dimensional commutative associative Banach algebra. We prove theorems on the existence of a solution to this problem under different assumptions on the coefficient and free term of the problem, and give an explicit formula for the solution.