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Fourier inversion and the plancherel theorem

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Non Commutative Harmonic Analysis and Lie Groups

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 880))

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References

  1. W. Chao, Fourier inversion and the Plancherel formula for semi-simple Lie groups of real rank two, Ph.D. Thesis, University of Chicago, 1977.

    Google Scholar 

  2. Harish-Chandra, A formula for semisimple Lie groups, Amer. J. Math., 79 (1957), 733–760.

    Article  MathSciNet  MATH  Google Scholar 

  3. , Some results on an invariant integral on a semisimple Lie algebra, Ann. of Math., 80 (1964), 551–593.

    Article  MathSciNet  MATH  Google Scholar 

  4. , Discrete series for semisimple Lie groups I, Acta. Math., 113 (1965), 241–318.

    Article  MathSciNet  MATH  Google Scholar 

  5. , Harmonic analysis on real reductive groups III, Ann. of Math., 104 (1976), 117–201.

    Article  MathSciNet  MATH  Google Scholar 

  6. R. Herb, Character formulas for discrete series on semisimple Lie groups, Nagoya Math. J., 64 (1976), 47–61.

    Article  MathSciNet  MATH  Google Scholar 

  7. , Fourier inversion of invariant integrals on semisimple real Lie groups, Trans. Amer. Math. Soc., 249 (1979), 281–302.

    MathSciNet  MATH  Google Scholar 

  8. , Characters of averaged discrete series on semisimple real Lie groups, Pacific J. Math., 80 (1979), 169–177.

    Article  MathSciNet  MATH  Google Scholar 

  9. Fourier inversion and the Plancherel theorem for semisimple real Lie groups, to appear in Amer. J. Math.

    Google Scholar 

  10. Discrete series characters and Fourier inversion on semisimple real Lie groups, preprint (1980).

    Google Scholar 

  11. T. Hirai, Invariant eigendistributions of Laplace operators on real simple Lie groups IV, Japan J. Math., 3 (1977), 1–48.

    MathSciNet  MATH  Google Scholar 

  12. H. Midorikawa, On the explicit formulae of characters for discrete series representations, Japan J. Math., new ser. 3 (1977), 223–228.

    MathSciNet  MATH  Google Scholar 

  13. P. Sally and G. Warner, The Fourier transform on semisimple Lie groups of real rank one, Acta. Math., 131 (1973), 1–26.

    Article  MathSciNet  MATH  Google Scholar 

  14. M. Sugiura, Conjugate classes of Cartan subalgebras in real semisimple Lie algebras, J. Math. Soc. Japan, 11 (1959), 374–434.

    Article  MathSciNet  MATH  Google Scholar 

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Jacques Carmona Michèle Vergne

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© 1981 Springer-Verlag

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Herb, R.A. (1981). Fourier inversion and the plancherel theorem. In: Carmona, J., Vergne, M. (eds) Non Commutative Harmonic Analysis and Lie Groups. Lecture Notes in Mathematics, vol 880. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0090410

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  • DOI: https://doi.org/10.1007/BFb0090410

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-10872-6

  • Online ISBN: 978-3-540-38783-1

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