  The question of how to certify the non-negativity of a polynomial function
lies at the heart of Real Algebra and it also has important applications to
Optimization. In the setting of symmetric polynomials Timofte provided a useful
way of certifying non-negativity of symmetric polynomials that are of a fixed
degree. In this note we present more general results which naturally generalize
Timofte's setting. We investigate families of polynomials that allow special
representations in terms of power-sum polynomials.These in particular also
include the case of symmetric polynomials of fixed degree. Therefore, we
recover the consequences of Timofte's original statements as a corollary. Thus,
this note also provides an alternative and simple proof of Timofte's original
statements.
