Positive exponential sums and odd polynomials (CROSBI ID 189587)
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Podaci o odgovornosti
Slijepčević, Siniša ; Ninčević, Marina
engleski
Positive exponential sums and odd polynomials
Given an odd integer polynomial $f(x)$ of a degree $k\geq 3$, we construct a non-negative valued, normed trigonometric polynomial with the spectrum in the set of integer values of $f(x)$ not greater than $n$, and a small free coefficient $a_{; ; ; 0}; ; ; =O((\log n)^{; ; ; -1/k}; ; ; )$. This gives an alternative proof for the maximal possible cardinality of a set $A$, so that $A-A$ does not contain an element of $f(x)$. We also discuss other interpretations and an ergodic characterization of that bound.
Positive exponential sums; van der Corput sets; correlative sets; recurrence; difference sets; Fejer's kernel; positive definiteness
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Podaci o izdanju
18
2014.
35-54
objavljeno
1845-4100