论文标题
对傅立叶系数有限制的圆圈嵌入
Circle embeddings with restrictions on Fourier coefficients
论文作者
论文摘要
本文继续研究圆圈的几何形状与其傅立叶系数的值之间的关系。首先，我们回答了Kovalev和Yang的一个问题，内容涉及星光嵌入的傅立叶变换的支持。圆圈嵌入的一个重要特殊情况是圆圈的同态形态。在单方面的傅立叶支持下，这种同构是与Blaschke产品相关的合理功能。我们研究理性圆的同态同态的结构，并表明它们在统一拓扑中形成了连接的集合。
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.
