TY - JOUR
T1 - The Krzyż Conjecture and an Entropy Conjecture
AU - Agler, Jim
AU - McCarthy, John E.
N1 - Publisher Copyright:
© 2021, The Hebrew University of Jerusalem.
PY - 2021/12
Y1 - 2021/12
N2 - We show that if the minimum entropy for a polynomial with roots on the unit circle is attained by polynomials with equally spaced roots, then, under a generic hypothesis about the nature of the extremum, the Krzyz conjecture on the maximum modulus of the Taylor coefficients of a holomorphic function that maps the disk to the punctured disk is true.
AB - We show that if the minimum entropy for a polynomial with roots on the unit circle is attained by polynomials with equally spaced roots, then, under a generic hypothesis about the nature of the extremum, the Krzyz conjecture on the maximum modulus of the Taylor coefficients of a holomorphic function that maps the disk to the punctured disk is true.
UR - http://www.scopus.com/inward/record.url?scp=85121297249&partnerID=8YFLogxK
U2 - 10.1007/s11854-021-0178-z
DO - 10.1007/s11854-021-0178-z
M3 - Article
AN - SCOPUS:85121297249
SN - 0021-7670
VL - 144
SP - 207
EP - 226
JO - Journal d'Analyse Mathematique
JF - Journal d'Analyse Mathematique
IS - 1
ER -