Transformation de Fourier sur l'espace de Schwartz d'un espace symétrique réductif

The Plancherel decomposition for a reductive symmetric space. I. Spherical functions

“…Remark 13.10 At the end of the sequel to this paper, [15], we will show that the normalized Eisenstein integral introduced above coincides (up to a change from ν to −ν) with the one introduced by J. Carmona and P. Delorme in [19].…”

“…His results have appeared in a series of papers, partly in collaboration with J. Carmona, [19], [23], [24]. At the time of the announcement we relied on the theorem of Carmona and Delorme on the Maass-Selberg relations for Eisenstein integrals, [19], Thm. 2, which in turn relied on Delorme's paper [23].…”

A Paley–Wiener theorem for reductive symmetric spaces

“…The generalized Eisenstein integrals we use were introduced in [6]; they are smooth functions on X. It is shown in [9] that they are matrix coefficients of nonminimal principal series representations and that they agree with the generalized Eisenstein integrals of [12]. However, these facts play no role here.…”

Eisenstein integrals and induction of relations

“…16.3, see also [4]. The result has been generalized to c-functions associated with arbitrary σθ-stable parabolic subgroups by P. Delorme [24], see also [19]. It plays a crucial role in Delorme's proof of the Plancherel formula, see [25], as well in the proof of the Plancherel formula by myself and Schlichtkrull, see [13] and [14].…”