This paper formulates a spatially-limited signal energy concentration problem on the 2-sphere using a generalized moment criterion in the spectral domain. The set of optimal signals with maximum concentration for general positive spherical harmonic coefficient frequency weightings is obtained. Numerically solving the resulting integral equation optimization shows that this set of functions not only decays slower but also has higher sidelobes than the set of spherical Slepian functions. This result on the 2-sphere contrasts with the findings from the time-frequency analogy which compares the classical Slepian eigenfunctions with the minimum bandwidth basis functions for the fourth-moment bandwidth measure.
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