Aspects of Harmonic Analysis on Real Hyperbolic Space

Abstract

In settings with rich geometric structure e. g. Euclidean space and symmetric spaces associated with Lie groups, harmonic analysis is naturally interpreted as the investigation of function like entities via synthesis and decomposition formulas expressed in terms of eigenfunctions of operators intrinsically related to this structure, i.e. invariant differential operators. This interpretation has been made manifest in recent works of Strichartz [18], [20], [21], aspects of which have been generalized and applied by Bray [1], [2], and in the realm of symmetric spaces much work remains. In this paper we examine the basic questions and ideas in the case of real n-dimensional hyperbolic space.

Topics & Concepts