Asymptotic Behaviour of Elementary Spherical Functions

Abstract

This chapter, as well as the next one, will be devoted to the formulation and proofs of the main theorems of the L² harmonic analysis of spherical functions. At the center of the theory is the Harish-Chandra transform (see §3.3)

$$f \mapsto Hf$$

where

$$f Hf(\lambda ) = \int\limits_G {f(x)\varphi (\lambda :x)dx.} $$