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The Harish-Chandra Series and Spherical Inversion

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

Abstract

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.

Keywords

Haar Measure Spherical Function Polynomial Growth Chapter Versus Iwasawa Decomposition 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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