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Extreme values of the derivative of Blaschke products and hypergeometric polynomials
- Source :
- Bull. Sci. Math. 169 (2021), 102979
- Publication Year :
- 2020
-
Abstract
- 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.<br />Comment: Corrected typos, added references
- Subjects :
- Mathematics - Complex Variables
Primary 30J10, Secondary 33C05, 33C45
Subjects
Details
- Database :
- arXiv
- Journal :
- Bull. Sci. Math. 169 (2021), 102979
- Publication Type :
- Report
- Accession number :
- edsarx.2007.09760
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1016/j.bulsci.2021.102979