  In the present paper, we introduce the multidimensional Clifford prolate
spheroidal wave functions (CPSWFs) defined on the unit ball as eigenfunctions
of a Clifford differential operator and provide a Galerkin method for their
computation as linear combinations of Clifford-Legendre polynomials. We show
that these functions are
  eigenfunctions of the truncated Fourier transformation. Then we investigate
the role of the CPSWFs in the spectral concentration problem associated with
balls in the space and frequency domains, the behaviour of the eigenvalues of
the time-frequency limiting operator and their spectral accumulation property.
