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- W2963072012 abstract "The first purpose of this article is to provide conditions for a bounded operator in L2(Rn) to be the Weyl (resp. anti-Wick) quantization of a bounded continuous symbol on R2n. Then, explicit formulas for the Weyl (resp. anti-Wick) symbol are proved. Secondly, other formulas for the Weyl and anti-Wick symbols involving a kind of Campbell Hausdorff formula are obtained. A point here is that these conditions and explicit formulas depend on the dimension n only through a Gaussian measure on R2n of variance 1/2 in the Weyl case (resp. variance 1 in the anti-Wick case) suggesting that the infinite dimension setting for these issues could be considered. Besides, these conditions are related to iterated commutators recovering in particular the Beals characterization Theorem. Nous donnons dans cet article des conditions pour qu'un opérateur borné dans L2(Rn) soit associé par la quantification de Weyl (resp. d'anti-Wick) à un symbole sur R2n continu et borné. Nous déterminons alors des formules explicites pour ce symbole de Weyl (resp. d'anti-Wick). Ensuite, nous obtenons d'autres expressions pour ces deux symboles, en relation avec la formule de Campbell Hausdorff. Ces conditions et formules explicites dépendent de la dimension n uniquement à travers une mesure Gaussienne de variance 1/2 dans le cas de la quantification de Weyl et de variance 1 pour le cas anti-Wick, laissant supposer la possibilité de considérer ces problèmes en dimension infinie. De plus, ces conditions sont également en relation avec des commutateurs itérés, ce qui permet de retrouver en particulier le Théorème de caractérisation de Beals." @default.
- W2963072012 created "2019-07-30" @default.
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- W2963072012 date "2019-10-01" @default.
- W2963072012 modified "2023-10-09" @default.
- W2963072012 title "Integral formulas for the Weyl and anti-Wick symbols" @default.
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- W2963072012 doi "https://doi.org/10.1016/j.matpur.2019.01.007" @default.
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