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Description: |
Vlad Timofte proved in 2001/2 that a symmetric real polynomial F of degree d in n variables is nonnegative on certain subsets of Rn if and only if it is so on the subset of points with at most max{|_d/2_|,2} distinct components. His proof used ordinary differential equations. Quite recently Cordian Riener found an elementary proof for this `half degree principle' using hyperbolic polynomials in one variable. We report on these ideas which as a spinoff allow to infer a claim concerning the minima of linear combinations of elementary symmetric polynomials which was published in 1987 with an apparently irreparably flawed argument. Joint work with Cordian Riener and Salma Kuhlmann.
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