Polynomial Interpolation on the Unit Sphere II

Abstract

The problem of interpolation at $(n+1{)}^2$ points on the unit sphere ${\mathbb{S}}^2$ by spherical polynomials of degree at most $n$ is proved to have a unique solution for several sets of points. The points are located on a number of circles on the sphere with even number of points on each circle. The proof is based on a method of factorization of polynomials.

14 pages