Decay of matrix coefficients on reductive homogeneous spaces of spherical type

Abstract

Let \(Z\) be a homogeneous space \(Z=G/H\) of a real reductive Lie group \(G\) with a reductive subgroup \(H\). The investigation concerns the quantitative decay of matrix coefficients on \(Z\) under the assumption that \(Z\) is of spherical type, that is, minimal parabolic subgroups have open orbits on \(Z\).