Vanishing of Certain Equivariant Distributions on p-Adic Spherical Spaces, and Nonvanishing of Spherical Bessel Functions.

We prove vanishing of distribution on p-adic spherical spaces that are equivariant with respect to a generic character of the nilradical of a Borel subgroup and satisfy a certain condition on the wave-front set. We deduce from this nonvanishing of spherical Bessel functions for Galois symmetric pairs. [ABSTRACT FROM AUTHOR]