A Striktpositivstellensatz for measurable functions

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. To cite this article: M. Putinar, C R. Acad. Sci. Paris, Ser. I347 (2009). (C) 2009 Academie des sciences. Published by Elsevier Masson SAS. All rights reserved.