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Extending the Archimedean Positivstellensatz to the Non-Compact Case

  • M. Marshall (a1)
Abstract

A generalization of Schmüdgen’s Positivstellensatz is given which holds for any basic closed semialgebraic set in (compact or not). The proof is an extension of Wörmann’s proof.

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References
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[1] Acquistapace, F., Andradas, C. and Broglia, F., The strict Positivstellensatz for global analytic functions and the moment problem for semianalytic sets. preprint.
[2] Andradas, C., Bröcker, L. and Ruiz, J. M., Constructible sets in real geometry. Ergeb Math., Springer, Berlin, Heidelberg, New York, 1996.
[3] Becker, E. and Schwartz, N., Zum Darstellungssatz von Kadison-Dubois. Arch. Math. 39 (1983), 421428.
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[8] Marshall, M., A real holomorphy ring without the Schmüdgen property. Canad. Math. Bull. 42 (1999), 354358.
[9] Monnier, J. P., Anneaux d’holomorphie et Positivstellensatz archimédien. Manuscripta Math. 97 (1998), 269302.
[10] Putinar, M., Positive polynomials on compact semi-algebraic sets. Indiana Univ.Math. J. 42 (1993), 969984.
[11] Schmüdgen, K., The K-moment problem for compact semialgebraic sets. Math. Ann. 289 (1991), 203206.
[12] Stengle, G., A Nullstellensatz and a Positivstellensatz in semialgebraic geometry. Math. Ann. 207 (1974), 6797.
[13] Wörmann, T., Short algebraic proofs of theorems of Schmüdgen and Pólya. preprint.
[14] Wörmann, T., Strikt positive Polynome in der semialgebraischen Geometrie. PhD Thesis, Dortmund, 1998.
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Canadian Mathematical Bulletin
  • ISSN: 0008-4395
  • EISSN: 1496-4287
  • URL: /core/journals/canadian-mathematical-bulletin
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