Decay on homogeneous spaces of reductive type

In this paper we explore homogeneous spaces Z=G/H of a a real reductive Lie group G with a closed connected subgroup H. The investigation concerns the decay at infinity of smooth functions on Z, and L^p-integrability of matrix coefficients. These results are used in a study of the asymptotic density of lattice points on Z. Explicit examples are given of spaces for which results are new.

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