PORTUGALIAE MATHEMATICA Vol. 56, No. 2, pp. 169194 (1999) 

Microlocal Tempered Inverse Image and Cauchy ProblemFrancesco ToninInstitut de Mathématiques, Analyse Algébrique, Université Pierre et Marie Curie, Case 82,4, place Jussieu, F75252 Paris Cedex 05  FRANCE Email: 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. Full text of the article:
Electronic version published on: 31 Jan 2003. This page was last modified: 27 Nov 2007.
© 1999 Sociedade Portuguesa de Matemática
