Abstract :
In this paper, which is a continuation of [V. Timofte, On the positivity of symmetric polynomial
functions. Part I: General results, J. Math. Anal. Appl. 284 (2003) 174–190] and [V. Timofte, On the
positivity of symmetric polynomial functions. Part II: Lattice general results and positivity criteria
for degrees 4 and 5, J. Math. Anal. Appl., in press], we study properties of extremal polynomials of
degree 4, and we give the construction of some of them. The main results are Theorems 9, 13, 15,
16, and 18.
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