Invariant harmonic analysis on split rank one groups with applications (Q1062149)

Let G be a real connected noncompact semisimple Lie group with finite center. We assume that if \(G_{{\mathbb{C}}}\) is the simply connected complex analytic Lie group with Lie algebra \({\mathfrak g}_{{\mathbb{C}}}\), then \(G\subset G_{{\mathbb{C}}}\). Fix a maximal compact subgroup K of G. Assume further that \(rk(G/K)=1\). This paper has two principal sections. In Section I we characterize the invariant transforms of functions in \({\mathcal C}^ p(G:F)\) (F\(\subset K\), \(| F| <\infty)\); Section II deals with the characterization of the orbital integrals of such functions.