Hardy Spaces of Meta-Analytic Functions and the Schwarz Boundary Value Problem

TL;DR

This paper extends representation formulas for meta-analytic functions, generalizing the similarity principle of the Vekua equation, and solves a higher-order Schwarz boundary value problem with distributional boundary conditions.

Contribution

It introduces new representation formulas for meta-analytic functions and addresses a generalized Schwarz boundary value problem with distributional boundary conditions.

Findings

Extended the similarity principle to meta-analytic functions

Solved a higher-order Schwarz boundary value problem in this context

Provided new tools for boundary value problems with distributional data

Abstract

We extend representation formulas that generalize the similarity principle of solutions to the Vekua equation to certain classes of meta-analytic functions. Also, we solve a generalization of the higher-order Schwarz boundary value problem in the context of meta-analytic functions with boundary conditions that are boundary values in the sense of distributions.