Invariant harmonic analysis on split rank one groups with applications
type: Item
instance of: scholarly article
title: Invariant harmonic analysis on split rank one groups with applications
zbMATH Open document ID: 0572.22005
author: P. C. Trombi
published in: Pacific Journal of Mathematics
publication date: 1982-01-01T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 22E30
Mathematics Subject Classification ID: 22E45
zbMATH DE Number: 3912658
zbMATH Keywords: split rank one groups
zbMATH Keywords: noncompact semisimple Lie group
zbMATH Keywords: invariant transforms
zbMATH Keywords: orbital integrals
MaRDI profile type: Publication
full work available at URL: pjm.1982.101.223
OpenAlex ID: W2032297676
DOI: 10.2140/PJM.1982.101.223
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description: scientific article; zbMATH DE number 3912658