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Transformation de Fourier géométrique. I. (French) Zbl 0553.14005

Given a complex of sheaves on a real vector bundle E, homogeneous (in a suitable sense) in the fibers of \(E\setminus \{0\}\), one defines another complex of sheaves on the dual bundle \(E^*\). This operator is closely related to the ”microlocalization” in the sense of Sato. It is a geometric analogue to the Fourier transform and has properties similar to it: inversion formula, Plancherel formula, etc..

MSC:

14F05 Sheaves, derived categories of sheaves, etc. (MSC2010)
43A32 Other transforms and operators of Fourier type
46M20 Methods of algebraic topology in functional analysis (cohomology, sheaf and bundle theory, etc.)
46F12 Integral transforms in distribution spaces
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