Pacific Journal of Mathematics

The Schwartz space of a general semisimple Lie group. V. Schwartz class wave packets.

Rebecca A. Herb

Article information

Source
Pacific J. Math., Volume 174, Number 1 (1996), 43-139.

Dates
First available in Project Euclid: 6 December 2004

Permanent link to this document
https://projecteuclid.org/euclid.pjm/1102365363

Mathematical Reviews number (MathSciNet)
MR1398373

Zentralblatt MATH identifier
0861.22007

Subjects
Primary: 22E46: Semisimple Lie groups and their representations

Citation

Herb, Rebecca A. The Schwartz space of a general semisimple Lie group. V. Schwartz class wave packets. Pacific J. Math. 174 (1996), no. 1, 43--139. https://projecteuclid.org/euclid.pjm/1102365363


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References

  • [CM] W. Casselman and D. Milicic, Asymptotic behavior of matrix coefficients of admis- sible representations, Duke Math. J., 49 (1982), 869-930.
  • [HC1] Harish-Chandra, Harmonic analysis on real reductive groups I, J. Funct. Anal., 19 (1975), 104 -204.
  • [HC2] Harish-Chandra, Harmonic analysis on real reductive groups II, Inv. Math., 36 (1976), 1-55.
  • [HC3] Harish-Chandra, Harmonic analysis on real reductive groups III, Annals of Math., 104 (1976), 117-201.
  • [HI] R. Herb, The Schwartz space of a general semisimple Lie group II, Wave packets associated to Schwartz functions, Trans. AMS., 327 (1991), 1-69.
  • [H2] R. Herb, The Schwartz space of a general semisimple Lie group III, c-functions, Advances in Math., 99 (1993), 1-25.
  • [H3] R. Herb, The Schwartz space of a general semisimple Lie group IV,Elementary mixed wave packets, Compositio Math., 84 (1992), 115-209.
  • [HW1] R. Herb and J. Wolf, The Plancherel theorem for general semisimple groups, Com- positio Math., 57 (1986),271-355.
  • [HW2] R. Herb and J. Wolf, Rapidly decreasing functions on general semisimple groups, Compositio Math., 58 (1986),73-110.
  • [HW3] R. Herb and J. Wolf, Wave packets for the relative discrete series I: The holomorphic case, J. Funct. Anal., 73 (1987), 1-37.
  • [HW4] R. Herb and J. Wolf, Wave packets for the relative discrete series II: The non-holomorphic case, J. Funct. Anal., 73 (1987),38-106.
  • [HW5] R. Herb and J. Wolf, The Schwartz space of a general semisimple group I, Wave packets of Eisen- stein integrals, Advances in Math., 80 (1990), 164-224.
  • [KM] H. Kraljevic and D. Milicic, The C*-algebra of the universal covering group of 5L(2,R), Glasnik Mat. Ser. Ill, 7(27) (1972), 35-48.
  • [S] W. Schmid, Two character identities for semisimple Lie groups, (Proc. Marseille Conf., 1976) Lecture Notes in Math., Vol. 587, Springer-Verlag, Berlin and New York, 1977.
  • [W] J. Wolf, Unitary representations on partially holomorphic cohomology spaces,Mem- oirs A.M.S., 138 (1974).

See also

  • Rebecca A. Herb, Joseph A. Wolf. The Schwartz space of a general semisimple Lie group. I. Wave packets of Eisenstein integrals. I [MR 91j:22013] Adv. Math. 80 1990 2 164--224.
  • Rebecca A. Herb. The Schwartz space of a general semisimple Lie group. {II}. Wave packets associated to Schwartz functions. II [MR 91m:22023] Trans. Amer. Math. Soc. 327 1991 1 1--69.
  • Rebecca A. Herb. The Schwartz space of a general semisimple Lie group. {III}. {$c$}-functions. III [MR 94g:22032] Adv. Math. 99 1993 1 1--25.
  • Rebecca A. Herb. The Schwartz space of a general semisimple Lie group. {IV}. Elementary mixed wave packets. IV [MR 94g:22033] Compositio Math. 84 1992 2 115--209.