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analyse pseudo-différentielle p-adique

Abstract : We develop the pseudodifferential analysis of operators acting on complex--valued functions on k?, where k is a non--Archimedean field. Our study relies on the generalization of classical concepts such as the the Weyl calculus and Heisenberg's representation, also on the characterization of classes of operators by means of their action on "families of coherent states". A Beals--type characterization of certain classes of operators, together with the usual application to a functional calculus of operators of weight one, is derived as a consequence. Since no derivation operators are available in the p--adic analysis, no Moyal--style expansion of the composition of two symbols is possible: nevertheless, using the theory of multiplicative characters of k^(×), we give a composition formula expressing the decomposition in "homogeneous terms" of a sharp--product f?f? in terms of the corresponding decompositions of the two factors.
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https://tel.archives-ouvertes.fr/tel-00002546
Contributor : Abdellah Bechata <>
Submitted on : Tuesday, June 3, 2003 - 6:40:08 PM
Last modification on : Thursday, January 30, 2020 - 3:54:04 PM
Long-term archiving on: : Monday, September 20, 2010 - 11:27:59 AM

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  • HAL Id : tel-00002546, version 2

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Abdellah Bechata. analyse pseudo-différentielle p-adique. Mathématiques [math]. Université de Reims - Champagne Ardenne, 2001. Français. ⟨tel-00002546v2⟩

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