Portugaliae Mathematica   EMIS ELibM Electronic Journals PORTUGALIAE
Vol. 56, No. 2, pp. 169-194 (1999)

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Microlocal Tempered Inverse Image and Cauchy Problem

Francesco Tonin

Institut de Mathématiques, Analyse Algébrique, Université Pierre et Marie Curie, Case 82,
4, place Jussieu, F-75252 Paris Cedex 05 -- FRANCE
E-mail: tonin@math.jussieu.fr

Abstract: We prove an inverse image formula for the functor $\tmhom(\cdot,{\cal O})$ of Andronikof \cite{A}, that is, the microlocalization of the functor $\TH(\cdot,{\cal O})$ of tempered cohomology introduced by Kashiwara. As an application, following an approach initiated by D'Agnolo and Schapira, we study the tempered ramified linear Cauchy problem. We deal with ramifications of logarithmic type, or along a swallow's tail subvariety, or at the boundary of the data existence domain.

Keywords: $\cal D$-mo\-du\-les; Cauchy problem; tempered cohomology.

Classification (MSC2000): 32C38, 32S40, 35A10.

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Electronic version published on: 31 Jan 2003. This page was last modified: 27 Nov 2007.

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