Univalent approximation by Fourier series of step functions

TL;DR

This paper demonstrates that univalent harmonic mappings can be effectively approximated using Fourier series composed of step functions, advancing the understanding of approximation methods in complex analysis.

Contribution

It introduces a novel approximation technique for univalent harmonic mappings using Fourier series of step functions, which was not previously established.

Findings

Univalent harmonic mappings can be approximated by Fourier series of step functions.

The approximation preserves univalence in the harmonic mappings.

The method provides a new tool for complex analysis and approximation theory.

Abstract

We prove that univalent harmonic mappings can be approximated by univalent Fourier series of step functions.