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The symbol of a function of a pseudo-differential operator

Alfonso Gracia-saz — 2005

Annales de l'institut Fourier

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 A 𝒞 ( 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 .

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