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arXiv · 1403.3783

Some Positivstellensätze for polynomial matrices

Công-Trình Lê
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Abstract

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,...,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 (\r^{d}) with respect to a subset (\hoa{G}) of polynomial matrices and the Archimedean property of the preordering and the quadratic module generated by (\hoa{G}).

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Công-Trình Lê. 2014-10-15. Some Positivstellensätze for polynomial matrices. https://doi.org/10.1007/s11117-014-0312-6

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