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On the Plancherel measure for linear Lie groups of rank one

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Abstract

In this paper we find a very explicit, simple form for the Plancherel measure for rank one, linear simple groups, including the normalizing constant.

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References

  1. BOURBAKI: Elements de Mathematique, Groupes et algébres de Lie, Chap. 4-6, Paris, Hermann (1968)

    Google Scholar 

  2. KNAPP, A. and STEIN, E.: Intertwining operators for semi-simple groups, Ann. of Math. 93, 489–578 (1971)

    Google Scholar 

  3. MIATELLO, R.: The Minakshisundaram-Pleijel coefficients for the vector valued heat kernel on compact. locally symmetric spaces of negative curvature. To appear in Transactions of the A.M.S.

  4. OKAMOTO, K.: On the Plancherel formulas for some types of simple Lie groups, Osaka J. Math. 2, 247–282 (1965)

    Google Scholar 

  5. RADER, C.: Invariant polynomials and spherical functions. To appear in Boletim da Sociedade Brasileira de Matemática

  6. WALLACH, N. R.: Harmonic Analysis on homogeneous spaces, 1st edn, New York, M. Dekker (1973)

    Google Scholar 

  7. WARNER, G.: Harmonic Analysis on semi-simple Lie groups I and II, 1st edition, New York, Springer-Verlag (1972)

    Google Scholar 

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Miatello, R.J. On the Plancherel measure for linear Lie groups of rank one. Manuscripta Math 29, 249–276 (1979). https://doi.org/10.1007/BF01303630

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  • DOI: https://doi.org/10.1007/BF01303630

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