Hilbert Boundary Value Problems for Hyper Monogenic Functions on The Hyperplane

TL;DR

This paper addresses Hilbert boundary value problems for hyper monogenic functions on hyperplanes, providing explicit solutions and solvability conditions, with novel negative order cases even in the complex plane.

Contribution

It introduces explicit solution formulas and solvability conditions for hyper monogenic boundary value problems, including new negative order cases.

Findings

Explicit solution formulas for hyper monogenic boundary value problems

Solvability conditions for these boundary value problems

Extension of results to negative order cases in complex analysis

Abstract

This paper systematically studies Hilbert boundary value problems for hyper monogenic functions on the hyperplane for the solutions being of any integer orders at the infinity, where the negative order cases are new even when restricted to the complex plane context. The explicit solution formulas are given and the solvability conditions are specified. The results are proved through using the Clifford symmetric extension method to reduce Hilbert boundary value problems to Riemann boundary value problems.