Vol. 101, No. 1, 1982

Recent Issues
Vol. 307: 1  2
Vol. 306: 1  2
Vol. 305: 1  2
Vol. 304: 1  2
Vol. 303: 1  2
Vol. 302: 1  2
Vol. 301: 1  2
Vol. 300: 1  2
Online Archive
Volume:
Issue:
     
The Journal
Subscriptions
Editorial Board
Officers
Contacts
 
Submission Guidelines
Submission Form
Policies for Authors
 
ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
Special Issues
Author Index
To Appear
 
Other MSP Journals
Invariant harmonic analysis on split rank one groups with applications

P. C. Trombi

Vol. 101 (1982), No. 1, 223–245
Abstract

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
Milestones
Received: 10 July 1980
Revised: 5 January 1981
Published: 1 July 1982
Authors
P. C. Trombi