The symbol of a function of a pseudo-differential operator
[Le symbole d'une fonction d'un opérateur pseudo-différentiel]
Annales de l'Institut Fourier, Tome 55 (2005) no. 7, pp. 2257-2284.

On obtient une formule explicite pour le symbole d’une fonction d’un opérateur. À partir d’un opérateur pseudo-différentiel A ^ sur L 2 ( N ) avec symbole A𝒞 (T * N ) et une fonction lisse f, nous obtenons le symbole de f(A ^) en termes de A. Comme application, les règles de quantification de Bohr-Sommerfeld sont calculées explicitement à l’ordre 4 en .

We give an explicit formula for the symbol of a function of an operator. Given a pseudo-differential operator A ^ on L 2 ( N ) with symbol A𝒞 (T * N ) and a smooth function f, we obtain the symbol of f(A ^) in terms of A. As an application, Bohr-Sommerfeld quantization rules are explicitly calculated at order 4 in .

DOI : 10.5802/aif.2161
Classification : 53D55, 81S10
Keywords: Deformation quantization, Moyal product, Weyl quantization, Bohr-Sommerfeld, symbol, diagrammatic technique, Deformation quantization, Moyal product, Weyl quantization, Bohr-Sommerfeld, symbol, diagrammatic technique
Mot clés : quantification par déformation, produit de Moyal, quantification de Weyl, Bohr-Sommerfeld, symbole, technique diagrammatique
Gracia-saz, Alfonso 1

1 University of California at Berkeley, Department of Mathematics, Berkeley CA 94720-3840 (USA)
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Gracia-saz, Alfonso. The symbol of a function of a pseudo-differential operator. Annales de l'Institut Fourier, Tome 55 (2005) no. 7, pp. 2257-2284. doi : 10.5802/aif.2161. http://www.numdam.org/articles/10.5802/aif.2161/

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