TY - JOUR
T1 - Extreme values of the derivative of Blaschke products and hypergeometric polynomials
AU - Kovalev, Leonid V.
AU - Yang, Xuerui
N1 - Publisher Copyright:
© 2021 Elsevier Masson SAS
PY - 2021/7
Y1 - 2021/7
N2 - 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.
AB - 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.
KW - Finite Blaschke product
KW - Hardy space
KW - Hypergeometric function
KW - Hypergeometric polynomial
KW - Poisson kernel
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U2 - 10.1016/j.bulsci.2021.102979
DO - 10.1016/j.bulsci.2021.102979
M3 - Article
AN - SCOPUS:85103769773
SN - 0007-4497
VL - 169
JO - Bulletin des Sciences Mathematiques
JF - Bulletin des Sciences Mathematiques
M1 - 102979
ER -