@article{104a6ff30f194711891e78b20c0c452e,
title = "Circle embeddings with restrictions on Fourier coefficients",
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.",
keywords = "Blaschke products, Circle embeddings, Circle homeomorphisms, Rational functions",
author = "Liulan Li and Kovalev, {Leonid V.}",
note = "Funding Information: The work of Leonid Kovalev was supported by the National Science Foundation grant DMS-1764266 . The work of Liulan Li was partly supported by the Science and Technology Plan Project of Hunan Province (No. 2016TP1020 ), and the Application-Oriented Characterized Disciplines, Double First-Class University Project of Hunan Province (Xiangjiaotong [2018]469 ). Funding Information: The work of Leonid Kovalev was supported by the National Science Foundation grant DMS-1764266. The work of Liulan Li was partly supported by the Science and Technology Plan Project of Hunan Province (No. 2016TP1020), and the Application-Oriented Characterized Disciplines, Double First-Class University Project of Hunan Province (Xiangjiaotong [2018]469). The authors thank the anonymous referee for several suggestions which improved the organization of this article. Publisher Copyright: {\textcopyright} 2020 Elsevier Inc.",
year = "2020",
month = aug,
day = "15",
doi = "10.1016/j.jmaa.2020.124083",
language = "English (US)",
volume = "488",
journal = "Journal of Mathematical Analysis and Applications",
issn = "0022-247X",
publisher = "Academic Press Inc.",
number = "2",
}