Comptes Rendus
no. 7-8
Functional Analysis
A Striktpositivstellensatz for measurable functions
[Un Striktpositivstellensatz pour les fonctions mesurables]

Présenté par : Michel Raynaud

Mihai Putinar1
1 Mathematics Department, University of California, Santa Barbara, CA 93106, USA
Comptes Rendus. Mathématique, Volume 347 (2009) no. 7-8, pp. 381-384.
est référencé par Corrigendum to the Note “A Striktpositivstellensatz for measurable functions” [C. R. Acad. Sci. Paris, Ser. I 347 (7–8) (2009) 381–384]

La décomposition dans une somme de carrés ponderés d'une fonction de Borel positive sur un ensemble mesurable est obtenue grace au théorème spectral pour les systemes commutatifs des opérateurs autoadjoints. Un résultat similaire, obtenu pour les pôlynomes ou certaines fonctions rationelles a été fortement exploité au cours des dernières douze années pour l'optimisation non-lineaire et non-convexe.

A weighted sums of squares decomposition of positive Borel measurable functions on a bounded Borel subset of the Euclidean space is obtained via duality from the spectral theorem for tuples of commuting self-adjoint operators. The analogous result for polynomials or certain rational functions was amply exploited during the last decade in a variety of applications.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2009.02.010
Mihai Putinar 1

1 Mathematics Department, University of California, Santa Barbara, CA 93106, USA 
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Mihai Putinar. A Striktpositivstellensatz for measurable functions. Comptes Rendus. Mathématique, Volume 347 (2009) no. 7-8, pp. 381-384. doi : 10.1016/j.crma.2009.02.010. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2009.02.010/

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☆ Partially supported by the National Science Foundation-USA.

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