11 citations · 16 across the 6 of their papers we have counts for
6 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…
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…
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…
Differential-difference operators and radial part formulas for non-invariant elements
Hiroshi Oda
The classical radial part formula for the invariant differential operators and the K-invariant functions on a Riemannian symmetric space G/K is generalized to some non-invariant ca…
Generalization of Harish-Chandra's basic theorem for Riemannian symmetric spaces of non-compact type
Hiroshi Oda
A basic exact sequence by Harish-Chandra related to the invariant differential operators on a Riemannian symmetric space G/K is generalized for each K-type in a certain class which…
Minimal polynomials and annihilators of generalized Verma modules of the scalar type
Hiroshi Oda, Toshio Oshima
Let g be a complex reductive Lie algebra and U(g) the universal enveloping algebra of g. Associated to a faithful irreducible finite dimensional representation of g, a square matri…