Transformationsgruppen mit affinen Bahnen. (Transformation groups with affine orbits)
type: Item
instance of: scholarly article
title: Transformationsgruppen mit affinen Bahnen. (Transformation groups with affine orbits)
zbMATH Open document ID: 0582.58037
DOI: 10.1007/BF01458455
published in: Mathematische Annalen
publication date: 1986-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/164141
review text: Let G be a connected Lie group acting on \({\mathbb{R}}^ n\) in such a manner that all orbits are affine and that the Euclidean measures on the orbits are G-invariant. In this paper there are given explicit disintegrations of invariant measures and distributions, respectively, over the set of Euclidean measures. In the case of linear group actions the Euclidean measures are closely related with invariant eigendistributions of invariant differential operators with constant coefficients. Thus the disintegrations provide eigendistribution expansions. The eigendistribution expansions on Heisenberg groups given by \textit{L. P. Rothschild} and \textit{J. A. Wolf} [Indiana Univ. Math. J. 25, 753-762 (1976; Zbl 0353.22007)] are received as a special case. Furthermore, from our disintegration formula we derive necessary and sufficient conditions for certain invariant differential equations to have invariant solutions.
Mathematics Subject Classification ID: 58J70
Mathematics Subject Classification ID: 57S25
Mathematics Subject Classification ID: 43A85
zbMATH DE Number: 3932068
zbMATH Keywords: Lie group acting on \({\mathbb{R}}^ n\)
zbMATH Keywords: disintegrations of invariant measures
zbMATH Keywords: invariant eigendistributions of invariant differential operators
author: Rainer Felix
MaRDI profile type: Publication
cites work: Q3925570
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OpenAlex ID: W1977345953
description: scientific article; zbMATH DE number 3932068