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   -> Volume 6, Issue 1

Preprint: Wavelet Approximations on Closed Surfaces
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Frank Schneider (

PostPosted: Thu Jan 16, 1997 1:39 pm    
Subject: Preprint: Wavelet Approximations on Closed Surfaces
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#6 Preprint: Wavelet Approximations on Closed Surfaces

Authors: W. Freeden, F. Schneider

Title: Wavelet Approximations on Closed Surfaces
and Their Application to Boundary-value Problems
of Potential Theory

Abstract: Wavelets on closed surfaces in Euclidean space $ R^3 $ are
introduced starting from a scale discrete wavelet transform for
potentials harmonic down to a spherical boundary. Essential tools for
approximation are integration formulas relating an integral over the
sphere to suitable linear combinations of functional values
(resp. normal derivatives) on the closed surface under consideration.
A scale discrete version of multiresolution is described for potential
functions harmonic outside the closed surface and regular at
infinity. Furthermore, an exact fully discrete wavelet approximation
is developed in case of band-limited wavelets. Finally, the role of
wavelets is discussed in three problems, namely (i) the representation
of a function on a closed surface from discretely given data, (ii) the
(discrete) solution of the exterior Dirichlet problem, and (iii) the
(discrete) solution of the exterior Neumann problem.

This preprint is available at


Best regards

W. Freeden, F. Schneider

Prof. Dr. Willi Freeden email:
Dipl.-Math. Frank Schneider email:
Department of Mathematics fax: ++49 631 29081
Geomathematics Group
University of Kaiserslautern
P.O. Box 3049
D-67653 Kaiserslautern
All times are GMT + 1 Hour
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