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The category of enhanced subanalytic sheaves as a tool for Fourier analysis
Dubussy, Christophe


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Keywords :
Laplace transform; subanalytic sheaves; algebraic analysis
Abstract :
[en] In this talk, we introduce the category of enhanced subanalytic sheaves on a complex bordered space by using the subanalytic site and the addition of an extra real variable. We also define Grothendieck operations and convolution functors which allow to see this category as a commutative tensor category. Then, we consider a bordered complex vector space and we define enhanced Fourier-Sato functors, which are equivalence of categories. We finally explain how this framework allows to obtain a "device" which produces explicit holomorphic Paley-Wiener-type theorems thanks to cohomological computations.
Disciplines :
Author, co-author :
Dubussy, Christophe ;  Université de Liège - ULiège > Département de mathématique > Analyse algébrique
Language :
Title :
The category of enhanced subanalytic sheaves as a tool for Fourier analysis
Publication date :
04 February 2019
Event name :
Category Theory Seminar
Event organizer :
Université catholique de Louvain
Event place :
Louvain-La-Neuve, Belgium
Event date :
4 octobre 2019
Funders :
F.R.S.-FNRS - Fonds de la Recherche Scientifique [BE]
Available on ORBi :
since 05 February 2019


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