5 papers
Fourier transforms related to a root system of rank 1
Wolter Groenevelt
We introduce an algebra consisting of difference-reflection operators and multiplication operators that can be considered as a analogue of Sahi's double affine H…
Wilson function transforms related to Racah coefficients
Wolter Groenevelt
The irreducible -representations of the Lie algebra consist of discrete series representations, principal unitary series and complementary series. We calculate Racah c…
The Wilson function transform
Wolter Groenevelt
Two unitary integral transforms with a very-well poised -function as a kernel are given. For both integral transforms the inverse is the same as the original transform after…
Laguerre functions and representations of su(1,1)
Wolter Groenevelt
Spectral analysis of a certain doubly infinite Jacobi operator leads to orthogonality relations for confluent hypergeometric functions, which are called Laguerre functions. This do…
Continuous Hahn functions as Clebsch-Gordan coefficients
Wolter Groenevelt, Erik Koelink, Hjalmar Rosengren
An explicit bilinear generating function for Meixner-Pollaczek polynomials is proved. This formula involves continuous dual Hahn polynomials, Meixner-Pollaczek functions, and non-p…