TY - JOUR
T1 - Hilbert transforms and the equidistribution of zeros of polynomials
AU - Carneiro, Emanuel
AU - Das, Mithun Kumar
AU - Florea, Alexandra
AU - Kumchev, Angel V.
AU - Malik, Amita
AU - Milinovich, Micah B.
AU - Turnage-Butterbaugh, Caroline
AU - Wang, Jiuya
N1 - Publisher Copyright:
© 2021 Elsevier Inc.
PY - 2021/11/1
Y1 - 2021/11/1
N2 - We improve the current bounds for an inequality of Erdős and Turán from 1950 related to the discrepancy of angular equidistribution of the zeros of a given polynomial. Building upon a recent work of Soundararajan, we establish a novel connection between this inequality and an extremal problem in Fourier analysis involving the maxima of Hilbert transforms, for which we provide a complete solution. Prior to Soundararajan (2019), refinements of the discrepancy inequality of Erdős and Turán had been obtained by Ganelius (1954) and Mignotte (1992).
AB - We improve the current bounds for an inequality of Erdős and Turán from 1950 related to the discrepancy of angular equidistribution of the zeros of a given polynomial. Building upon a recent work of Soundararajan, we establish a novel connection between this inequality and an extremal problem in Fourier analysis involving the maxima of Hilbert transforms, for which we provide a complete solution. Prior to Soundararajan (2019), refinements of the discrepancy inequality of Erdős and Turán had been obtained by Ganelius (1954) and Mignotte (1992).
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U2 - 10.1016/j.jfa.2021.109199
DO - 10.1016/j.jfa.2021.109199
M3 - Article
AN - SCOPUS:85111741771
SN - 0022-1236
VL - 281
JO - Journal of Functional Analysis
JF - Journal of Functional Analysis
IS - 9
M1 - 109199
ER -