Interpolatory Band-Limited Wavelet Bases on the Sphere

What is it about?

In the present paper, we construct space-localized bases for a wavelet-like space W^n of band-limited functions on the sphere. Each of the basis functions is a zonal polynomial centered at a point η_i ∈ S^2. The goal of this work is to describe explicit fundamental systems {η_j}j=1,...,M_n for the space W^n which finally lead to space- and frequency-localized polynomial bases for L^2(S^2).

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