Slepian Spatial-Spectral Concentration on the Ball

Understand

We formulate and solve the Slepian spatial-spectral concentration problem on the three-dimensional ball.

• Both the standard Fourier-Bessel and also the Fourier-Laguerre spectral domains are considered since the latter exhibits a number of practical advantages (spectral decoupling and exact computation).
• The Slepian spatial and spectral concentration problems are formulated as eigenvalue problems, the eigenfunctions of which form an orthogonal family of concentrated functions.
• Equivalence between the spatial and spectral problems is shown.