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.
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.
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@article{CRMATH_2014__352_12_1017_0, author = {Barthe, Franck and Wolff, Pawe{\l}}, 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}, url = {http://www.numdam.org/articles/10.1016/j.crma.2014.09.016/} }
TY - JOUR AU - Barthe, Franck AU - Wolff, Paweł TI - Positivity improvement and Gaussian kernels JO - Comptes Rendus. Mathématique PY - 2014 SP - 1017 EP - 1021 VL - 352 IS - 12 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2014.09.016/ DO - 10.1016/j.crma.2014.09.016 LA - en ID - CRMATH_2014__352_12_1017_0 ER -
%0 Journal Article %A Barthe, Franck %A Wolff, Paweł %T Positivity improvement and Gaussian kernels %J Comptes Rendus. Mathématique %D 2014 %P 1017-1021 %V 352 %N 12 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2014.09.016/ %R 10.1016/j.crma.2014.09.016 %G en %F CRMATH_2014__352_12_1017_0
Barthe, Franck; Wolff, Paweł. Positivity improvement and Gaussian kernels. Comptes Rendus. Mathématique, Tome 352 (2014) no. 12, pp. 1017-1021. doi : 10.1016/j.crma.2014.09.016. http://www.numdam.org/articles/10.1016/j.crma.2014.09.016/
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