9 citations · 13 across the 8 of their papers we have counts for
10 papers
Inversion formula for the hypergeometric Fourier transform associated with a root system of type
Tatsuo Honda, Hiroshi Oda, Nobukazu Shimeno
We give the inversion formula and the Plancherel formula for the hypergeometric Fourier transform associated with a root system of type , when the multiplicity parameters are n…
An extension of Pizzetti's formula associated with the Dunkl operators
Nobukazu Shimeno, Naoya Tani
We give an extension of Pizzetti's formula associated with the Dunkl operators. It gives an explicit formula for the Dunkl inner product of an arbitrary function and a homogeneous…
Spherical inversion for a small -type on the split real Lie group of type
Hiroshi Oda, Nobukazu Shimeno
We give an explicit formula for the Harish-Chandra -function for a small -type on a split real Lie group of type . As an application we give an explicit formula for sphe…
Hobson's formula for Dunkl operators and its applications
Nobukazu Shimeno
We generalize classical Hobson's formula concerning partial derivatives of radial functions on a Euclidean space to a formula in the Dunkl analysis. As applications we give new sim…
The hypergeometric function for the root system of type with a certain degenerate parameter
Nobukazu Shimeno, Yuichi Tamaoka
We express explicitly the Heckman-Opdam hypergeometric function for the root system of type A with a certain degenerate parameter in terms of the Lauricella hypergeometric function…
Spherical functions for small -types
Hiroshi Oda, Nobukazu Shimeno
For a connected semisimple real Lie group of non-compact type, Wallach introduced a class of -types called small. We classify all small -types for all simple Lie groups a…