Vol. 101, No. 1, 1982

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Invariant harmonic analysis on split rank one groups with applications

P. C. Trombi

Vol. 101 (1982), No. 1, 223–245

Let G be a real connected noncompact semisimple Lie group with finite center; we shall denote the algebras of Lie groups L by the corresponding lower case German letter, l. We assume that if Gc is the simply connected complex analytic Lie group with Lie algebra gc (here for any vector space V defined over R we denote its complexification by V c; in particular gc is the complexification of g) then G Gc. Fix a maximal compact subgroup K of G. Assume further that rk(G∕K) = 1. This paper has two principal sections. In §I we characterize the invariant transforms of functions in 𝒞p(G : F)(F K,|F| < ); §II deals with the characterization of the orbital integrals of such functions.

Mathematical Subject Classification 2000
Primary: 22E30
Secondary: 22E45
Received: 10 July 1980
Revised: 5 January 1981
Published: 1 July 1982
P. C. Trombi