Trombi, P. C. Invariant harmonic analysis on split rank one groups with applications. (English) Zbl 0572.22005 Pac. J. Math. 101, 223-245 (1982). 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. Cited in 1 ReviewCited in 8 Documents MSC: 22E30 Analysis on real and complex Lie groups 22E45 Representations of Lie and linear algebraic groups over real fields: analytic methods Keywords:split rank one groups; noncompact semisimple Lie group; invariant transforms; orbital integrals PDFBibTeX XMLCite \textit{P. C. Trombi}, Pac. J. Math. 101, 223--245 (1982; Zbl 0572.22005) Full Text: DOI