Extreme values of the derivative of Blaschke products and hypergeometric polynomials

Leonid V. Kovalev, Xuerui Yang

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish (US)
Article number102979
JournalBulletin des Sciences Mathematiques
Volume169
DOIs
StatePublished - Jul 2021

Keywords

  • Finite Blaschke product
  • Hardy space
  • Hypergeometric function
  • Hypergeometric polynomial
  • Poisson kernel

ASJC Scopus subject areas

  • Mathematics(all)

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