A: New Wavelet Methods for Approximating Harmonic Functions; B: Satellite Gradiometry - from Mathematical and Numerical Point of View

  • Some new approximation methods are described for harmonic functions corresponding to boundary values on the (unit) sphere. Starting from the usual Fourier (orthogonal) series approach, we propose here nonorthogonal expansions, i.e. series expansions in terms of overcomplete systems consisting of localizing functions. In detail, we are concerned with the so-called Gabor, Toeplitz, and wavelet expansions. Essential tools are modulations, rotations, and dilations of a mother wavelet. The Abel-Poisson kernel turns out to be the appropriate mother wavelet in approximation of harmonic functions from potential values on a spherical boundary.

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Metadaten
Author:Willi Freeden, Michael Schreiner
URN (permanent link):urn:nbn:de:hbz:386-kluedo-5069
Serie (Series number):Berichte der Arbeitsgruppe Technomathematik (AGTM Report) (109)
Document Type:Preprint
Language of publication:English
Year of Completion:1995
Year of Publication:1995
Publishing Institute:Technische Universität Kaiserslautern
Source:F. Sanso, editor, Geodetic Theory Today, International Association of Geodesy Symposia 114, Springer (1995)
Faculties / Organisational entities:Fachbereich Mathematik
DDC-Cassification:510 Mathematik

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