Special Functions in Mathematical Geosciences: An Attemptat a Categorization

  • Willi Freeden
  • Michael Schreiner
Living reference work entry

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This chapter reports on the current activities and recent progress in the field of special functions of mathematical geosciences. The chapter focuses on two major topics of interest, namely, trial systems of polynomial (i.e., spherical harmonics) and polynomially based (i.e., zonal kernel) type. A fundamental tool is an uncertainty principle, which gives appropriate bounds for both the qualification and quantification of space and frequency (momentum) localization of the special (kernel) function under consideration. The essential outcome is a better understanding of constructive approximation in terms of zonal kernel functions such as splines and wavelets.


Spherical Harmonic Uncertainty Principle Pseudodifferential Operator Frequency Localization Space Domain 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Geomathematics GroupUniversity of KaiserslauternRhineland-PalatinateGermany
  2. 2.Institute for Computational EngineeringUniversity of BuchsBuchsSwitzerland

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