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.
Jury, Robert TW Martin, Sub-Hardy-Hilbert Spaces in the Non-commutative Unit Row Ball , in: Function Spaces, Theory and Applications, pp
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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.