On quotient measures and induced representations
type: Item
instance of: scholarly article
title: On quotient measures and induced representations
zbMATH Open document ID: 0677.43006
DOI: 10.1016/0022-247X(89)90215-1
author: Z. Magyar
published in: Journal of Mathematical Analysis and Applications
publication date: 1989-01-01T00:00:00Z
review text: Let G be a locally compact group and H a closed subgroup of G. A function \(\rho\) : \(G\to {\mathbb{C}}\) is called a \(\rho\)-function if it satisfies the condition \(\rho (hg)=\delta (h)\Delta (h)^{-1}\rho (g)\) for all \(h\in H\) and \(g\in G\), where \(\delta\) and \(\Delta\) are the modular functions of H and G respectively. The author shows the existence of continuous \(\rho\)-functions and, as a consequence, positive Radon measures m on the quotient space whose translates \(m_ g\) have continuous Radon-Nikodym derivatives with respect to m. This observation allows a somewhat simpler proof of Mackey's intertwining theorem on induced representations.
Mathematics Subject Classification ID: 43A65
Mathematics Subject Classification ID: 22D30
Mathematics Subject Classification ID: 43A05
zbMATH DE Number: 4109335
zbMATH Keywords: locally compact group
zbMATH Keywords: modular functions
zbMATH Keywords: continuous \(\rho\)-functions
zbMATH Keywords: positive Radon measures
zbMATH Keywords: continuous Radon-Nikodym derivatives
zbMATH Keywords: Mackey's intertwining theorem on induced representations
MaRDI profile type: Publication
cites work: On Induced Representations
cites work: On a theorem of G. W. Mackey
cites work: Q5723435
cites work: Q5270328
cites work: Positive definite functions and induced representations
cites work: Induced representation of locally compact groups. I
cites work: Induced representations and a new proof of the imprimitivity theorem
description: scientific article; zbMATH DE number 4109335