# Hilbert transforms and the equidistribution of zeros of polynomials

@inproceedings{Carneiro2021HilbertTA, title={Hilbert transforms and the equidistribution of zeros of polynomials}, author={Emanuel Carneiro and Mithun Kumar Das and Alexandra Florea and Angel V. Kumchev and Amita Malik and Micah B. Milinovich and Caroline L. Turnage-Butterbaugh and Jiuya Wang}, year={2021} }

## 3 Citations

A Hybrid Signal Processing Technique for Recognition of Complex Power Quality Disturbances

- EngineeringElectric Power Systems Research
- 2022

Generalized Erd\H{o}s-Tur\'an inequalities and stability of energy minimizers

- Mathematics
- 2021

Abstract The classical Erdős-Turán inequality on the distribution of roots for complex polynomials can be equivalently stated in a potential theoretic formulation, that is, if the logarithmic…

The Sharp Erd\H{o}s-Tur\'an Inequality

- Mathematics
- 2021

Erdős and Turán proved a classical inequality on the distribution of roots for a complex polynomial in 1950, depicting the fundamental interplay between the size of the coefficients of a polynomial…

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Using Fourier analysis, a short and self-contained proof of a classical result of Erdős and Turán that if a monic polynomial has small size on the unit circle and its constant coefficient is not too small, then its zeros cluster near the unitcircle and become equidistributed in angle.

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A Remark on the Arcsine Distribution and the Hilbert transform

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A localized Parseval-type identity is proved that seems to be new: if f(x)(1-x^2)1/4∈L2(-1,1) and its Hilbert transform Hf vanishes on (-1, 1), then the function f is a multiple of the arcsine distribution.

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Given two intervals $I, J \subset \mathbb{R}$, we ask whether it is possible to reconstruct a real-valued function $f \in L^2(I)$ from knowing its Hilbert transform $Hf$ on $J$. When neither interval…

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Basic Forms x n dx = 1 n + 1 x n+1 (1) 1 x dx = ln |x| (2) udv = uv − vdu (3) 1 ax + b dx = 1 a ln |ax + b| (4) Integrals of Rational Functions 1 (x + a) 2 dx = −

SOME EXTREMAL FUNCTIONS IN FOURIER ANALYSIS

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Moreover, he showed that there is equality in (1.4) if and only if F(z) = B(z). As an application Beurling found an interesting inequahty for almost periodic functions (we include it here in Theorem…

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Prolegomena. 1. L p Spaces and Interpolation. 2. Maximal Functions, Fourier Transform, and Distributions. 3. Fourier Analysis on the Torus. 4. Singular Integrals of Convolution Type. 5.…