Circle embeddings with restrictions on Fourier coefficients
Complex Variables
2020-04-02 v2
Abstract
This paper continues the investigation of the relation between the geometry of a circle embedding and the values of its Fourier coefficients. First, we answer a question of Kovalev and Yang concerning the support of the Fourier transform of a starlike embedding. An important special case of circle embeddings are homeomorphisms of the circle onto itself. Under a one-sided bound on the Fourier support, such homeomorphisms are rational functions related to Blaschke products. We study the structure of rational circle homeomorphisms and show that they form a connected set in the uniform topology.
Cite
@article{arxiv.2002.03192,
title = {Circle embeddings with restrictions on Fourier coefficients},
author = {Liulan Li and Leonid V. Kovalev},
journal= {arXiv preprint arXiv:2002.03192},
year = {2020}
}