Spherical Harmonics Based Special Function Systems and Constructive Approximation Methods

  • Willi Freeden
  • Volker Michel
  • Frederik J. Simons
Part of the Geosystems Mathematics book series (GSMA)


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’.


Spherical harmonics procedures Slepian spline and wavelet methods regularized functional matching pursuit 


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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Willi Freeden
    • 1
  • Volker Michel
    • 2
  • Frederik J. Simons
    • 3
  1. 1.Geomathematics GroupUniversity of KaiserslauternKaiserslauternGermany
  2. 2.Geomathematics GroupUniversity of SiegenSiegenGermany
  3. 3.Department of GeosciencesPrinceton UniversityPrincetonUSA

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