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2002/2003 On the gaps between zeros of trigonometric polynomials.
Gady Kozma, Ferencz Oravecz
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Real Anal. Exchange 28(2): 447-454 (2002/2003).


We show that for every finite set \(0\notin S\subset \mathbb{Z}^{d}\) with the property \(-S=S\), every real trigonometric polynomial \(f\) on the \(d\) dimensional torus \(\mathbb{T}^{d}=\mathbb{R}^{d}/\mathbb{Z}^{d}\) with spectrum in \(S\) has a zero in every closed ball of diameter \(D\left(S\right)\), where \(D\left(S\right)=\sum _{\lambda \in S}\frac{1}{4||\lambda ||_{2}}\), and investigate tightness in some special cases.


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Gady Kozma. Ferencz Oravecz. "On the gaps between zeros of trigonometric polynomials.." Real Anal. Exchange 28 (2) 447 - 454, 2002/2003.


Published: 2002/2003
First available in Project Euclid: 20 July 2007

zbMATH: 1050.42001
MathSciNet: MR2009766

Primary: 26C10 , 30C15 , 42A05 , 42B99

Keywords: roots , trigonometric polynomials , Zeros

Rights: Copyright © 2002 Michigan State University Press

Vol.28 • No. 2 • 2002/2003
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