Sufficient conditions for sampling and interpolation on the sphere

Abstract

We obtain sufficient conditions for arrays of points, $\mathcal{Z}=\{\mathcal{Z}(L){\}}_{L\ge 1},$ on the unit sphere $\mathcal{Z}(L)\subset {\mathbb{S}}^d,$ to be Marcinkiewicz-Zygmund and interpolating arrays for spaces of spherical harmonics. The conditions are in terms of the mesh norm and the separation radius of $\mathcal{Z}(L)$.