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.

中文翻译：

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对傅立叶系数有限制的圆嵌入

摘要 本文继续研究圆嵌入的几何形状与其傅立叶系数值之间的关系。首先，我们回答 Kovalev 和 Yang 关于支持星状嵌入的傅立叶变换的问题。圆嵌入的一个重要特例是圆自身的同胚。在傅里叶支持的单边约束下，这种同胚是与 Blaschke 积相关的有理函数。我们研究了有理圆同胚的结构，并表明它们在一致拓扑中形成了一个连通集。