The Harish-Chandra Series and Spherical Inversion

  • Jay Jorgenson
  • Serge Lang
Part of the Springer Monographs in Mathematics book series (SMM)


This chapter is fundamentally based on [Har 58a]. We define the Harish-Chandra series for eigenfunctions of Casimir, prove its basic properties, and show how the spherical functions can be expressed in terms of this series. We incorporate from the start a crucial estimate by Gangolli to insure the possibility of term by term differentiation [Gan 71]. The need for such an estimate had arisen in Helgason’s approach to getting the inversion theorem on the Paley-Wiener space [Hel 66]. The applications to the inversion problem will come in the next chapter.


Haar Measure Spherical Function Polynomial Growth Chapter Versus Iwasawa Decomposition 
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Copyright information

© Springer-Verlag New York, Inc. 2001

Authors and Affiliations

  • Jay Jorgenson
    • 1
  • Serge Lang
    • 2
  1. 1.Department of MathematicsCity College of New York, CUNYNew YorkUSA
  2. 2.Department of MathematicsYale UniversityNew HavenUSA

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