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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Communicated by J.M. Peña and J. Carnicer
Dedicated to Mariano Gasca on the occasion of his 60th birthday
The second author was supported by the Graduate Program Applied Algorithmic Mathematics of the Munich University of Technology. The work of the third author was supported in part by the National Science Foundation under Grant DMS-0201669.
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zu Castell, W., Laín Fernández, N. & Xu, Y. Polynomial interpolation on the unit sphere II. Adv Comput Math 26, 155–171 (2007). https://doi.org/10.1007/s10444-005-7510-5
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DOI: https://doi.org/10.1007/s10444-005-7510-5