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

Abstract

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 $\mathbb{R}^d$, $d\geq 2$. 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.