Special Functions in Mathematical Geosciences: An Attempt at a Categorization

Willi Freeden () and Michael Schreiner
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Willi Freeden: University of Kaiserslautern, Geomathematics Group
Michael Schreiner: University of Buchs, Institute for Computational Engineering

A chapter in Handbook of Geomathematics, 2015, pp 2455-2482 from Springer

Abstract: 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.

Keywords: Radial Basis Function; Spherical Harmonic; Uncertainty Principle; Frequency Localization; Space Domain (search for similar items in EconPapers)
Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-54551-1_31

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DOI: 10.1007/978-3-642-54551-1_31

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