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Transformation de Mellin faisceautique et D-modules

Abstract : In a first part, we describe the complex of solutions of the algebraic Mellin transform of a D-module M in terms of the solutions of M. In order to do that, we define a Mellin transform functor on sheaves. We show the Mellin transform of the complex of fast decreasing solutions of a regular holonomic D-module M is quasi-isomorphic with the complex of solutions of the algebraic Mellin transform of M, the assumption of regularity not being necessary in the one variable case.
In a second part, we study the inverse Mellin transformation: our results are less complete. We define an inverse Mellin transform functor on sheaves. We show there are natural morphisms connecting the complex of solutions of the inverse algebraic Mellin transform of a finite difference module with the inverse Mellin transform of the complex of solutions with growth at most exponential of order 1 at infinity in vertical bands. We then show that, in the case of a one variable difference module with only one positive slope, these morphisms are isomorphisms.
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https://tel.archives-ouvertes.fr/tel-00133909
Contributor : Hervé Fabbro <>
Submitted on : Wednesday, February 28, 2007 - 10:21:27 AM
Last modification on : Wednesday, October 14, 2020 - 4:23:48 AM
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  • HAL Id : tel-00133909, version 1

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Hervé Fabbro. Transformation de Mellin faisceautique et D-modules. Mathématiques [math]. Université Nice Sophia Antipolis, 2006. Français. ⟨tel-00133909⟩

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