A noncompact group rep

Article View: sci.math.research

Article #11

#11

From: Allen Knutson
Date: Mon, 20 Jul 1992 03:36

9 lines
1046 bytes

Let G be locally compact, dg a nonzero Haar measure on G.

If G is compact (equivalently, \int_G dg is finite), then L^2(G) with G
acting by translation contains all the reps of G. If G is noncompact, it 
doesn't.

What about the space of functions that are L^2 on compact subsets of G?
That seems another natural generalization of the compact G case, and looks much
"bigger": what does it have?					Allen K.

Technical Details

Message-ID: <allenk.711603376@harry>

Path: arc1-ca.pugleaf.net!sparky!uunet!pmafire!news.dell.com!swrinde!sdd.hp.com!ux1.cso.uiuc.edu!news.cso.uiuc.edu!usenet

Show Full Headers

Complete Article Headers

Path: arc1-ca.pugleaf.net!sparky!uunet!pmafire!news.dell.com!swrinde!sdd.hp.com!ux1.cso.uiuc.edu!news.cso.uiuc.edu!usenet
From: allenk@harry.ugcs.caltech.edu (Allen Knutson)
Newsgroups: sci.math.research
Subject: A noncompact group rep
Keywords: noncompact group, L^2
Message-ID: <allenk.711603376@harry>
Date: 20 Jul 92 03:36:16 GMT
Sender: Daniel Grayson <dan@math.uiuc.edu>
Organization: California Institute of Technology, Pasadena
Lines: 9
Approved: Daniel Grayson <dan@math.uiuc.edu>
Nntp-Posting-Host: harry.ugcs.caltech.edu
X-Submissions-To: sci-math-research@uiuc.edu
X-Administrivia-To: sci-math-research-request@uiuc.edu