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Special Functions in Mathematical Geosciences: An Attempt at a Categorization

In: Handbook of Geomathematics

Author

Listed:
  • Willi Freeden

    (University of Kaiserslautern, Geomathematics Group)

  • Michael Schreiner

    (University of Buchs, Institute for Computational Engineering)

Abstract

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.

Suggested Citation

  • Willi Freeden & Michael Schreiner, 2015. "Special Functions in Mathematical Geosciences: An Attempt at a Categorization," Springer Books, in: Willi Freeden & M. Zuhair Nashed & Thomas Sonar (ed.), Handbook of Geomathematics, edition 2, pages 2455-2482, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-54551-1_31
    DOI: 10.1007/978-3-642-54551-1_31
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