Continuous Hahn Polynomials of Differential Operator Argument and Analysis on Riemannian Symmetric Spaces of Constant Curvature

@inproceedings{Badertscher2005ContinuousHP,
  title={Continuous Hahn Polynomials of Differential Operator Argument and Analysis on Riemannian Symmetric Spaces of Constant Curvature},
  author={Erich Badertscher and Tom H. Koornwinder},
  year={2005}
}
For the three types of simply connected Riemannian spaces of constant curvature it is shown that the associated spherical functions can be obtained from the corresponding (zonal) spherical functions by application of a differential operator of the form p(i d/dt), where p belongs to a system of orthogonal polynomials: Gegenbauer polynomials, Hahn polynomials or continuous symmetric Hahn polynomials. We give a group theoretic explanation of this phenomenon and relate the properties of the… CONTINUE READING