Circle embeddings with restrictions on Fourier coefficients

Research output: Contribution to journalArticle

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.

Original languageEnglish (US)
Article number124083
JournalJournal of Mathematical Analysis and Applications
Volume488
Issue number2
DOIs
StatePublished - Aug 15 2020

Keywords

  • Blaschke products
  • Circle embeddings
  • Circle homeomorphisms
  • Rational functions

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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