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On an extension of Pólyaʼs Positivstellensatz
Dickinson, Peter J. C., 1985- ; Povh, Janez, 1973-
In this paper we provide a generalization of a Positivstellensatz by Pólya [Pólya in Naturforsch Ges Zürich 73:141-145 1928]. We show that if a homogeneous polynomial is positive over the ...intersection of the non-negative orthant and a given basic semialgebraic cone (excluding the origin), then there exists a "Pólya type" certificate for non-negativity. The proof of this result uses the original Positivstellensatz by Pólya, and a Positivstellensatz by Putinar and Vasilescu [Putinar and Vasilescu C R Acad Sci Ser I Math 328(7) 1999].
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