Abstract
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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© 1995 Springer-Verlag Berlin Heidelberg
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Freeden, W., Schreiner, M. (1995). New Wavelet Methods for Approximating Harmonic Functions. In: Sansò, F. (eds) Geodetic Theory Today. International Association of Geodesy Symposia, vol 114. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-79824-5_22
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DOI: https://doi.org/10.1007/978-3-642-79824-5_22
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-59421-5
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