Some Positivstellensätze for polynomial matrices

Some Positivstellensätze for polynomial matrices In this paper we give a version of Krivine–Stengle’s Positivstellensatz, Schweighofer’s Positivstellensatz, Scheiderer’s local-global principle, Scheiderer’s Hessian criterion and Marshall’s boundary Hessian conditions for polynomial matrices, i.e. matrices with entries from the ring of polynomials in the variables $$x_1,\ldots ,x_d$$ x 1 , … , x d with real coefficients. Moreover, we characterize Archimedean quadratic modules of polynomial matrices, and study the relationship between the compactness of a subset in $$\mathbb R^{d}$$ R d with respect to a subset $$\mathcal {G}$$ G of polynomial matrices and the Archimedean property of the preordering and the quadratic module generated by $$\mathcal {G}$$ G . Positivity Springer Journals

Some Positivstellensätze for polynomial matrices

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Springer Basel
Copyright © 2014 by Springer Basel
Mathematics; Fourier Analysis; Operator Theory; Potential Theory; Calculus of Variations and Optimal Control; Optimization; Econometrics
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