Abstract
The structure of spherical harmonics allows us to develop a theory of best polynomial approximation on the sphere based essentially on multipliers, which is, historically, the first approach in this direction. It turns out that the entire framework based on multipliers can be established more generally for h-spherical harmonics associated with reflection-invariant weight functions developed in Chap. 7, which leads to a theory of weighted best approximation by polynomials that we shall present in its full generality.
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Dai, F., Xu, Y. (2013). Weighted Best Approximation by Polynomials. In: Approximation Theory and Harmonic Analysis on Spheres and Balls. Springer Monographs in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-6660-4_10
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DOI: https://doi.org/10.1007/978-1-4614-6660-4_10
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