Revisit on the Slepian concentration problem of the spherical Fourier-Bessel setup

In this paper, we will revisit the Slepian spatiospectral concentration problem for the spherical Fourier-Bessel band-limited spaces introduced for 3-D domain, and discuss its general form in ${\mathbb{R}}^d$, $d\ge 2$. In particular, we investigate the bimodal distribution of eigenvalues of the concentration operators and give an asymptotic characterization of the Shannon number given a linear relation between the Bessel bandwidth and spherical harmonic bandwidth.