  Given an odd integer polynomial f(x) of a degree k >=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.
