Circle embeddings with restrictions on Fourier coefficients

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:488

Article

Li, Liulan¹  Kovalev, Leonid, V² 

[1] Hengyang Normal Univ, Coll Math & Stat, Hengyang 421002, Hunan, Peoples R China

[2] Syracuse Univ, Dept Math, 215 Carnegie, Syracuse, NY 13244 USA

关键词: Circle embeddings;    Circle homeomorphisms;    Blaschke products;    Rational functions;   

DOI  :  10.1016/j.jmaa.2020.124083

来源: Elsevier

【 摘 要 】

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. (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

Free