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Polynomial Interpolation on the Unit Sphere II

Wolfgang zu Castell·Noemi Lain Fernandez·Yuan Xu
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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.

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Wolfgang zu Castell, Noemi Lain Fernandez, Yuan Xu. 2004-07-27. Polynomial Interpolation on the Unit Sphere II. https://arxiv.org/abs/math/0407448

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