Polynomial Bases on the Sphere
Considering that the well-known basis of spherical harmonics of degree at most n is not localized on the sphere, we construct better localized polynomial bases by means of reproducing kernels. Such a construction leads to the problem of finding sets of (n + 1)2 points on the sphere that admit unique polynomial interpolation. Finally, we present a possible construction of polynomial wavelets on the sphere.
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- Müller, C.: Spherical Harmonics, Springer: Berlin, Heidelberg, New York, (1966).Google Scholar
- Sündermann, B.: Projektionen auf Polynomräumen in mehreren Veränderlichen, Diss. Dortmund (1983).Google Scholar
- Xu, Y.: Polynomial Interpolation on the unit sphere,submitted.Google Scholar