An operator-valued Positivstellensatz equates positivity on matrix convex sets to a weighted sum-of-squares form, enabling an explicit sum-of-squares factorization for positive trigonometric polynomials on free products of finite abelian groups.
William Helton, Scott McCullough, Mihai Putinar, Engineering Systems and Free Semi-Algebraic Geometry , in: Emerging Applications of Algebraic Geometry, 17--62, IMA Vol
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Operator-Valued Positivstellens\"atze on Matrix Convex Sets and Free Products of Finite Abelian Groups
An operator-valued Positivstellensatz equates positivity on matrix convex sets to a weighted sum-of-squares form, enabling an explicit sum-of-squares factorization for positive trigonometric polynomials on free products of finite abelian groups.