Interpolatory band-limited wavelet bases on the sphere

In the present paper, we construct space-localized bases for the space W_nⁿ:= ⊕_k=n+1²ⁿ Harm _k (double-struck S sign²) of band-limited functions on the sphere. Each of the basis functions is a zonal polynomial centered at a point η_i ∈ double-struck S sign². The goal of this work is to describe explicit fundamental systems {η_j} _j=1,...,Mn for the space W_nⁿ which finally lead to space- and frequency-localized polynomial bases for L²(double- struck S sign²).