Abstract
We call a closed basic semialgebraic set \({X \subset \mathbb{R}^n}\) homogeneous if it is defined by a finite system of inequalities of the form \({g(x) \ge 0,}\) where \({g}\) is a homogeneous polynomial. We prove an effective version of the Putinar and Vasilescu Positivstellensatz for positive homogeneous polynomials on homogeneous semialgebraic sets.
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This research was partially supported by OPUS Grant No 2012/07/B/ST1/03293 (Poland), SONATA Grant No 2013/09/D/ST1/03701 (Poland) and ANR grant STAAVF (France).
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Gala-Jaskórzynska, A., Kurdyka, K., Kuta, K. et al. Positivstellensatz for homogeneous semialgebraic sets. Arch. Math. 105, 405–412 (2015). https://doi.org/10.1007/s00013-015-0822-x
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DOI: https://doi.org/10.1007/s00013-015-0822-x