## Real Analysis Exchange

### On the gaps between zeros of trigonometric polynomials.

#### Abstract

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.

#### Article information

Source
Real Anal. Exchange, Volume 28, Number 2 (2002), 447-454.

Dates
First available in Project Euclid: 20 July 2007

https://projecteuclid.org/euclid.rae/1184963807

Mathematical Reviews number (MathSciNet)
MR2009766

Zentralblatt MATH identifier
1050.42001

#### Citation

Kozma, Gady; Oravecz, Ferencz. On the gaps between zeros of trigonometric polynomials. Real Anal. Exchange 28 (2002), no. 2, 447--454. https://projecteuclid.org/euclid.rae/1184963807

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