Analysis on quasidisks; a unified approach through transmission and jump problems

TL;DR

This paper explores the mathematical properties of quasicircles by unifying concepts from geometric function theory, harmonic analysis, and approximation theory, focusing on transmission, jump problems, and singular integral operators.

Contribution

It introduces a unified framework for analyzing quasicircles through transmission and jump problems, connecting various mathematical tools and theories.

Findings

Characterization of quasicircles via boundary value problems

Connection between jump decomposition and singular integral operators

Approximation of quasicircles using Faber series

Abstract

We give an exposition of results from a crossroad between geometric function theory, harmonic analysis, boundary value problems and approximation theory, which characterize quasicircles. We will specifically expose the interplay between the jump decomposition, singular integral operators and approximation by Faber series. Our unified point of view is made possible by the the concept of transmission.