Extending the Archimedean Positivstellensatz to the Non-Compact Case
Canadian mathematical bulletin, Tome 44 (2001) no. 2, pp. 223-230

Voir la notice de l'article provenant de la source Cambridge University Press

A generalization of Schmüdgen’s Positivstellensatz is given which holds for any basic closed semialgebraic set in ${{\mathbb{R}}^{n}}$ (compact or not). The proof is an extension of Wörmann’s proof.
DOI : 10.4153/CMB-2001-022-2
Mots-clés : 12D15, 14P10, 44A60
Marshall, M. Extending the Archimedean Positivstellensatz to the Non-Compact Case. Canadian mathematical bulletin, Tome 44 (2001) no. 2, pp. 223-230. doi: 10.4153/CMB-2001-022-2
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[1] [1] Acquistapace, F., Andradas, C. and Broglia, F., The strict Positivstellensatz for global analytic functions and the moment problem for semianalytic sets. preprint. Google Scholar

[2] [2] Andradas, C., Bröcker, L. and Ruiz, J. M., Constructible sets in real geometry. Ergeb Math., Springer, Berlin, Heidelberg, New York, 1996. Google Scholar

[3] [3] Becker, E. and Schwartz, N., Zum Darstellungssatz von Kadison-Dubois. Arch. Math. 39 (1983), 421–428. Google Scholar

[4] [4] Berr, R. and Wörman, T., Positive polynomials and tame preorderings. Math. Z., (to appear). Google Scholar

[5] [5] Bochnak, J., Coste, M. and Roy, M. F., Géométrie Algébrique Réelle. Ergeb Math., Springer, Berlin, Heidelberg, New York, 1987. Google Scholar

[6] [6] Jacobi, T., A representation theorem for certain partially ordered commutative rings. Math. Z., (to appear). Google Scholar

[7] [7] Lam, T. Y., An introduction to real algebra. Rocky Mountain J. Math. 14 (1984), 767–814. Google Scholar

[8] [8] Marshall, M., A real holomorphy ring without the Schmüdgen property. Canad. Math. Bull. 42 (1999), 354–358. Google Scholar

[9] [9] Monnier, J. P., Anneaux d’holomorphie et Positivstellensatz archimédien. Manuscripta Math. 97 (1998), 269–302. Google Scholar

[10] [10] Putinar, M., Positive polynomials on compact semi-algebraic sets. Indiana Univ.Math. J. 42 (1993), 969–984. Google Scholar

[11] [11] Schmüdgen, K., The K-moment problem for compact semialgebraic sets. Math. Ann. 289 (1991), 203–206. Google Scholar

[12] [12] Stengle, G., A Nullstellensatz and a Positivstellensatz in semialgebraic geometry. Math. Ann. 207 (1974), 67–97. Google Scholar

[13] [13] Wörmann, T., Short algebraic proofs of theorems of Schmüdgen and Pólya. preprint. Google Scholar

[14] [14] Wörmann, T., Strikt positive Polynome in der semialgebraischen Geometrie. PhD Thesis, Dortmund, 1998. Google Scholar

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