Abstract
In the present paper, we construct space-localized bases for the space $W_n^n:=\oplus_{k=n+1}^{2n} Harm_k({\Bbb S}^2)$ of band-limited functions on the sphere. Each of the basis functions is a zonal polynomial centered at a point $\eta_i\in{\Bbb S}^2$. The goal of this work is to describe explicit fundamental systems $\lbrace\eta_j\rbrace_{j=1,\dots,M_n}$ for the space $W_n^n$ which finally lead to space- and frequency-localized polynomial bases for $L^2({\Bbb S}^2)$.
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Fernandez, N., Prestin, J. Interpolatory Band-Limited Wavelet Bases on the Sphere. Constr Approx 23, 79–101 (2005). https://doi.org/10.1007/s00365-005-0601-1
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DOI: https://doi.org/10.1007/s00365-005-0601-1