[Positivité améliorée et noyaux gaussiens]
We show that a positivity improving property of multilinear operators with Gaussian kernels can be determined, with sharp constants, by testing Gaussian functions only. This result can be considered as a reversed form of Lieb's theorem on maximizers of Gaussian kernels.
Nous montrons qu'une propriété d'amélioration de la positivité par les opérateurs multilinéaires à noyaux gaussiens peut être déterminée, avec des constantes exactes, en testant l'opérateur uniquement sur les fonctions gaussiennes. Ce résultat peut être considéré comme une forme inverse du théorème de Lieb sur les maximiseurs des noyaux gaussiens.
Accepté le :
Publié le :
Franck Barthe 1 ; Paweł Wolff 2, 3
@article{CRMATH_2014__352_12_1017_0, author = {Franck Barthe and Pawe{\l} Wolff}, title = {Positivity improvement and {Gaussian} kernels}, journal = {Comptes Rendus. Math\'ematique}, pages = {1017--1021}, publisher = {Elsevier}, volume = {352}, number = {12}, year = {2014}, doi = {10.1016/j.crma.2014.09.016}, language = {en}, }
Franck Barthe; Paweł Wolff. Positivity improvement and Gaussian kernels. Comptes Rendus. Mathématique, Volume 352 (2014) no. 12, pp. 1017-1021. doi : 10.1016/j.crma.2014.09.016. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2014.09.016/
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