Multiresolution on the Sphere

In this paper we study some basic tools for the construction of multi-scale systems on the unit sphere. Particularly, we emphasize properties of spherical harmonics and Legendre functions. Based on these orthogonal systems we discuss in some detail the decomposition of the classical Hilbert space on the sphere into subspaces of different level. To this end we explain different bases and frames. In our examples the building blocks consist of polynomials and spherical radial basis functions.

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