论文标题
Blaschke产品衍生物的极端值和高几何多项式
Extreme values of the derivative of Blaschke products and hypergeometric polynomials
论文作者
论文摘要
有限的Blaschke产品仅限于单位圆圈，是一个光滑的覆盖地图。该地图的衍生物的最大值和最小值反映了Blaschke产品的几何形状。我们确定了两类极端蓝菌产品：最大化衍生物的最大值和最小值之间的差异以及最小化衍生物之间的差异的产品。两种类都具有相同的代数结构，是两个超几何多项式的商。
A finite Blaschke product, restricted to the unit circle, is a smooth covering map. The maximum and minimum values of the derivative of this map reflect the geometry of the Blaschke product. We identify two classes of extremal Blaschke products: those that maximize the difference between the maximum and minimum of the derivative, and those that minimize it. Both classes turn out to have the same algebraic structure, being the quotient of two hypergeometric polynomials.
