Wave packets in the Schwartz space of a reductive p-adic symmetric space

Abstract

We form wave packets in the Schwartz space of a reductive p-adic symmetric space for certain famillies of tempered functions. We show how to construct such families from Eisenstein integrals.

We discovered a mistake in the proof of Theorem 2 in version 1. The second part of the proof was only allusive and not correct. In version 2, we change our definition of family of type I, I' and II' and give modified proofs of our main results (Theorems 4.6 and 5.1 in version 2, Theorems 1 and 2 in version 1) whose statements are essentially unchanged. The article will appear in J. of Lie Theory