Eisenstein integrals and induction of relations

Abstract

In this article I will give a survey of joint work with Henrik Schlichtkrull on the induction of certain relations among (partial) Eisenstein integrals for the minimal principal series of a reductive symmetric space. I will discuss the application of this principle of induction to the proof of the Fourier inversion formula in [11] and to the proof of the Paley-Wiener theorem in [15]. Finally, the relation with the Plancherel decomposition will be discussed.