On the gaps between zeros of trigonometric polynomials. (English) Zbl 1050.42001

Kozma, Gady; Oravecz, Ferencz

Real Anal. Exch. 28(2002-2003), No. 2, 447-454 (2003).

Authors’ abstract: “We show that for every finite set \(0\neq S\subset\mathbb{Z}^d\) 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 \(D(S)\), where \(D(S)= \sum_{\lambda\in S}{1\over 4\|\lambda\|_2}\), and investigate tightness in some special cases”.

Reviewer: Laszlo Leindler (Szeged)

MSC:

42A05	Trigonometric polynomials, inequalities, extremal problems
26C10	Real polynomials: location of zeros
30C10	Polynomials and rational functions of one complex variable
30C15	Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral)

Keywords:

trigonometric polynomial; tightness; zeros