Harmonic analysis on semisimple Lie groups

  title={Harmonic analysis on semisimple Lie groups},
  journal={Bulletin of the American Mathematical Society},
  • Harish-Chandra
  • Published 1 May 1970
  • Mathematics
  • Bulletin of the American Mathematical Society
Then tr 4̂ is actually independent of the choice of this base. Let VT denote the set of a l l /G^ i (G) such that ir(f) is of the trace class. Then Vr is a linear subspace of Li(G). Put 0 . ( / ) = tr *•(ƒ) ( f £ F T ) . Then ®T is a linear function on VT which we may call the character of 7T. Of course this concept would be useful only when the space V* is fairly large. Let 8(G) denote the set of all equivalence classes of irreducible unitary representations of G. It is easy to see that for… 
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