A Clifford Construction of Multidimensional Prolate Spheroidal Wave Functions

We investigate the construction of multidimensional prolate spheroidal wave functions using techniques from Clifford analysis. The prolates are defined to be eigenfunctions of a certain differential operator and we propose a method for computing these eigenfunctions through expansions in Clifford-Legendre polynomials. It is shown that the differential operator commutes with a time-frequency limiting operator defined relative to balls in n-dimensional Euclidean space.