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Internet Message Format  |  1992-07-22  |  1022 b 
  1. Path: sparky!uunet!pmafire!news.dell.com!swrinde!sdd.hp.com!ux1.cso.uiuc.edu!news.cso.uiuc.edu!usenet
  2. From: allenk@harry.ugcs.caltech.edu (Allen Knutson)
  3. Newsgroups: sci.math.research
  4. Subject: A noncompact group rep
  5. Keywords: noncompact group, L^2
  6. Message-ID: <allenk.711603376@harry>
  7. Date: 20 Jul 92 03:36:16 GMT
  8. Sender: Daniel Grayson <dan@math.uiuc.edu>
  9. Organization: California Institute of Technology, Pasadena
  10. Lines: 9
  11. Approved: Daniel Grayson <dan@math.uiuc.edu>
  12. Nntp-Posting-Host: harry.ugcs.caltech.edu
  13. X-Submissions-To: sci-math-research@uiuc.edu
  14. X-Administrivia-To: sci-math-research-request@uiuc.edu
  15.  
  16. Let G be locally compact, dg a nonzero Haar measure on G.
  17.  
  18. If G is compact (equivalently, \int_G dg is finite), then L^2(G) with G
  19. acting by translation contains all the reps of G. If G is noncompact, it 
  20. doesn't.
  21.  
  22. What about the space of functions that are L^2 on compact subsets of G?
  23. That seems another natural generalization of the compact G case, and looks much
  24. "bigger": what does it have?                    Allen K.
  25.