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Isoparametric polynomials and sums of squares

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 نشر من قبل Jianquan Ge
 تاريخ النشر 2018
  مجال البحث
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The Hilberts 17th problem asks that whether every nonnegative polynomial can be a sum of squares of rational functions. It has been answered affirmatively by Artin. However, as to the question whether a given nonnegative polynomial is a sum of squares of polynomials is still a central question in real algebraic geometry. In this paper, we solve this question completely for the nonnegative polynomials associated with isoparametric polynomials (initiated by E. Cartan) which define the focal submanifolds of the corresponding isoparametric hypersurfaces.



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