Positive Cubature formulas and Marcinkiewicz-Zygmund inequalities on spherical caps

Feng Dai, Heping Wang

Let ${\Pi }_n^d$ denote the space of all spherical polynomials of degree at most $n$ on the unit sphere $\sph$ of ${\mathbb{R}}^{d+1}$, and let $d(x,y)$ denote the usual geodesic distanc…