Harmonicity Modulus and Applications to the Approximation by Polyharmonic Functions

TL;DR

This paper introduces the harmonicity modulus and K-functional, then applies them to establish Jackson-type theorems for approximating continuous functions with polyharmonic functions.

Contribution

It presents new harmonicity measures and uses them to derive approximation theorems for polyharmonic functions, extending classical polynomial approximation results.

Findings

Established a Jackson-type theorem for polyharmonic approximation

Introduced harmonicity modulus and K-functional as new tools

Extended polynomial approximation results to polyharmonic functions

Abstract

In the present paper we introduce the notion of harmonicity modulus and harmonicity K-functional and apply these notions to prove a Jackson type theorem for approximation of continuous functions by polyharmonic functions. For corresponding results on approximation by polynomials see [3, 7].