Blaschke Products and Circumscribed Conics
Blaschke Products and Circumscribed Conics
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Blaschke 产品和外接圆锥曲线
DOI：
10.1007/s40315-017-0201-7
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发表时间：
2017
影响因子：
2.1
通讯作者：
Fujimura Masayo
中科院分区：
文献类型：
--
作者：
Masayo Fujimura;Parisa Hariri;Marcelina Mocanu;Matti Vuorinen;Masayo Fujimura;Fujimura Masayo
研究了有限Blaschke积的几何性质。对于B次的Blaschke积，设是在d次原像处与单位圆相切的直线的集合。我们证明了单位圆上每对两个元素的交点的迹线最多形成一条次数代数曲线。在低程度的情况下，我们有更精确的结果。例如，对于，迹线形成圆锥截面。对于，我们给出了Blaschke积的迹包含圆锥截线的一个充要条件。
We study geometrical properties of finite Blaschke products. For a Blaschke productBof degreed, letbe the set of the lines tangent to the unit circle at thedpreimages. We show that the trace of the intersection points of each pair of two elements inasranges over the unit circle forms an algebraic curve of degree at most. In case of low degree, we have more precise results. For instance, for, the trace forms a conic section. For, we provide a necessary and sufficient condition for Blaschke products whose trace include a conic section.