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Jacobi Functions and Analysis on Noncompact Semisimple Lie Groups

  • Tom H. Koornwinder
Part of the Mathematics and Its Applications book series (MAIA, volume 18)

Abstract

A Jacobi function \({\phi _\lambda }^{\left( {\alpha ,\beta } \right)}\left( {\alpha ,\beta ,\lambda \in C,\alpha \ne - 1, - 2,...} \right)\) is defined as the even C-function on ℝ which equals 1 at 0 and which satisfies the differential equation
$$\left( {{d^2}/d{t^2} + \left( {\left( {2\alpha + 1} \right)cotht + \left( {2\beta + 1} \right)tht} \right)d/dt + + {\lambda ^2} + {{\left( {\alpha + \beta + 1} \right)}^2}} \right){f_\lambda }^{\left( {\alpha ,\beta } \right)}\left( t \right) = 0.$$
(1.1)

Keywords

Symmetric Space Spherical Function Addition Formula Jacobi Function Plancherel Measure 
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

© D. Reidel Publishing Company 1984

Authors and Affiliations

  • Tom H. Koornwinder
    • 1
  1. 1.Centrum voor Wiskunde en InformaticaAmsterdamNederland

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