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

Brylinski, Jean-Luc; Malgrange, Bernard; Verdier, Jean-Louis

C. R. Acad. Sci., Paris, Sér. I 297, 55-58 (1983).

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

Keywords:

complex of sheaves; real vector bundle; dual bundle; microlocalization; Fourier transform; inversion formula; Plancherel formula