Spherical Harmonics Based Special Function Systems and Constructive Approximation Methods
Special function systems are reviewed that reflect particular properties of the Legendre polynomials, such as spherical harmonics, zonal kernels, and Slepian functions. The uncertainty principle is the key to their classification with respect to their localization in space and frequency/momentum. Methods of constructive approximation are outlined such as spherical harmonic and Slepian expansions, spherical spline and wavelet concepts. Regularized Functional Matching Pursuit is described as an approximation technique of combining heterogeneous systems of trial functions to a kind of a ‘best basis’.
Keywords.Spherical harmonics procedures Slepian spline and wavelet methods regularized functional matching pursuit
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