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Pré-Publication, Document De Travail Année : 2023

GEVREY WKB METHOD FOR PSEUDODIFFERENTIAL OPERATORS OF REAL PRINCIPAL TYPE

Richard Lascar
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Iván Moyano

Résumé

In this paper we investigate the conjugation of Fourier Integral Operators (FIOs) associated to Gevrey phases and symbols and the corresponding semiclassical pseudodifferential operators (pdos) in the Gevrey class. We obtain an Egorov theorem compatible with Gevrey FIOs and real principal part pdos with Gevrey symbols. As a consequence, we obtain a justification of the usual microlocal WKB expansion for Gevrey pdos which are of real principal part at a point in the phase space, with the natural Gevrey subexponential asymptotics with respect to the semiclassical parameter. Contents
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Dates et versions

hal-04046994 , version 1 (27-03-2023)

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  • HAL Id : hal-04046994 , version 1

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Richard Lascar, Iván Moyano. GEVREY WKB METHOD FOR PSEUDODIFFERENTIAL OPERATORS OF REAL PRINCIPAL TYPE. 2023. ⟨hal-04046994⟩
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