TY - JOUR
T1 - Extreme values of the derivative of Blaschke products and hypergeometric polynomials
AU - Kovalev, Leonid V.
AU - Yang, Xuerui
N1 - Funding Information:
We thank Pamela Gorkin for bringing the papers [9] and [11] to our attention, and the referee for many corrections and suggestions for improving the presentation. The work of Kovalev was supported by the National Science Foundation grant DMS-1764266. The work of Yang was supported by Young Research Fellow award from Syracuse University.
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 -