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 language | English (US) |
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Article number | 124083 |
Journal | Journal of Mathematical Analysis and Applications |
Volume | 488 |
Issue number | 2 |
DOIs | |
State | Published - Aug 15 2020 |
Keywords
- Blaschke products
- Circle embeddings
- Circle homeomorphisms
- Rational functions
ASJC Scopus subject areas
- Analysis
- Applied Mathematics