Uniqueness property for quasiharmonic functions

TL;DR

This paper introduces quasiharmonic functions, a class of continuous functions approximable by harmonic polynomials, and proves a uniqueness theorem similar to that for analytic functions.

Contribution

It establishes a new uniqueness property for quasiharmonic functions, expanding understanding of their behavior and approximation capabilities.

Findings

Proves a uniqueness theorem for quasiharmonic functions.

Defines quasiharmonic functions as those admitting best harmonic polynomial approximations.

Draws an analogy with the uniqueness properties of analytic functions.

Abstract

In this paper we consider class of continuous functions, called quasiaharmonic functions, admitting best approximations by harmonic polynomials. In this class we prove a uniqueness theorem by analogy with the analytic functions.