On Ces\`{a}ro and Abel-Poisson Means of Hexagonal Fourier Series

TL;DR

This paper investigates how Cesàro and Abel-Poisson means approximate functions with hexagonal symmetry, providing estimates based on the functions' smoothness, thereby advancing understanding of Fourier series in hexagonal lattices.

Contribution

The paper introduces new approximation estimates for Cesàro and Abel-Poisson means of hexagonal Fourier series, specifically relating approximation quality to the functions' modulus of continuity.

Findings

Approximation degree is estimated in terms of modulus of continuity.

Results apply to continuous, periodic functions on hexagonal lattices.

Provides theoretical bounds for approximation errors.

Abstract

Approximation properties of Ces\`{a}ro and Abel-Poisson means of hexagonal Fourier series are studied. The degree of approximation by these means of hexagonal Fourier series of functions, which are continuous and periodic with respect to the hexagon lattice, is estimated in terms of modulus of continuity of functions.