A Striktpositivstellensatz for measurable functions

Mihai Putinar

doi:10.1016/j.crma.2009.02.010

Functional Analysis

A Striktpositivstellensatz for measurable functions

Presented by: Michel Raynaud

Mihai Putinar ¹

¹ Mathematics Department, University of California, Santa Barbara, CA 93106, USA

Comptes Rendus. Mathématique, Volume 347 (2009) no. 7-8, pp. 381-384.

is referenced by Corrigendum to the Note “A Striktpositivstellensatz for measurable functions” [C. R. Acad. Sci. Paris, Ser. I 347 (7–8) (2009) 381–384]

Abstract
Résumé

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.

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.

Received: 2008-11-12
Accepted: 2009-02-03
Published online: 2009-02-28

DOI: 10.1016/j.crma.2009.02.010

Author's affiliations:

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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