Extreme values of the derivative of Blaschke products and hypergeometric polynomials

被引：0
|
作者：
Kovalev, Leonid, V [1 ]
Yang, Xuerui [1 ]
机构：
[1] Syracuse Univ, Dept Math, 215 Carnegie, Syracuse, NY 13244 USA
来源：
BULLETIN DES SCIENCES MATHEMATIQUES | 2021年 / 169卷
基金：
美国国家科学基金会;
关键词：
Finite Blaschke product; Hypergeometric function; Hypergeometric polynomial; Hardy space; Poisson kernel; ZEROS;
D O I：
10.1016/j.bulsci.2021.102979
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
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. (C) 2021 Elsevier Masson SAS. All rights reserved.
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页数：20
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