Les formules des traces relatives de Jacquet-Rallis grossi\`eres

Abstract

We establish the coarse relative trace formulae of Jacquet-Rallis for linear and unitary groups. Both formulae are of the form: a sum of spectral distributions equals a sum of geometric distributions. In order to obtain the spectral decompositions we introduce new truncation operators and we investigate their properties. On the geometric side, by means of the Cayley transform, the decompositions are derived from a procedure of descent to the tangent spaces for which the formulae are known thanks to our previous work.