Download:
|
by Willi Freeden, Frank Schneider
Problems of Potential Theory, Mathematical Methods in the Applied Sciences
http://www.mathematik.uni-kl.de/~wwwtecm/preprints/reports/report_171.ps.gz
Add To MetaCart
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 function 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.
Citations
|
137
|
Time–Frequency Analysis
– Cohen
- 1995
|
|
41
|
Foundations of Potential Theory
– Kellogg
- 1969
|
|
25
|
Nonstationary wavelets on the m-sphere for scattered data
– Narcowich, Ward
- 1996
|
|
14
|
Computing Fourier Transforms
– Driscoll, Healy
- 1994
|
|
10
|
Spherical Wavelets: Efficiently Representing
– Schroder, Sweldens
- 1995
|
|
8
|
Orthogonal and Nonorthogonal Multiresolution Analysis, Scale Discrete and Exact Fully Discrete Wavelet Transform on the Sphere, Constructive Approximation
– Freeden, Schreiner
- 1998
|
|
7
|
The Ohio State 1991 geopotential and sea surface topography harmonic coefficient models
– Rapp, Wang, et al.
- 1991
|
|
7
|
Phase space decompositions: Local Fourier analysis on spheres, preprint CPT93 /P.2878
– Torresani
- 1993
|
|
6
|
Uber eine Klasse von Integralformeln der Mathematischen Geodasie
– Freeden
- 1979
|
|
5
|
A spline interpolation method for solving boundary value problems of potential theory from discretely given data
– Freeden
- 1987
|
|
5
|
Spharische Wavelets: Theorie und Anwendung in der Physikalischen Geodasie
– Windheuser
- 1995
|
|
3
|
1885] Zur Theorie der eindeutigen analytischen Functionen
– Runge
|
|
3
|
Inverse Problems in Satellite Geodesy and Their Approximate Solution by Splines and Wavelets
– Schneider
- 1997
|
|
2
|
Spherical Wavelets and Their Application to Linear Inverse Satellite Problems, Diploma thesis
– Bayer
- 1996
|
|
2
|
A Continuous Wavelet Transform on Tangent Bundles of Spheres
– Dahlke, Maass
- 1994
|
|
2
|
On the Approximation of External Gravitational Potential With Closed Systems of (Trial
– Freeden
- 1980
|
|
2
|
Spherical Wavelet Transform and its
– Freeden, Windheuser
- 1996
|
|
2
|
On an Extension of Helly's Theorem
– Yamabe
- 1959
|
|
1
|
Spharische Wavelets und ihre numerische Realisation, Diploma thesis
– acker, M
- 1995
|
|
1
|
Least Square Approximation by Linear Combination of (Multi-)Poles
– Freeden
- 1983
|
|
1
|
A Constructive Approximation Theorem for the Oblique Derivative Problem of Potential Theory
– Freeden, Kersten
- 1981
|
|
1
|
Remainder Terms
– Freeden, Reuter
- 1982
|
|
1
|
Combined Spherical Harmonic and Wavelet
– Freeden, Windheuser
- 1995
|
|
1
|
Locally Supported Wavelets on the Sphere
– ottelmann, J
- 1996
|
|
1
|
Foundation of the Mathematical Theory of Electromagnetic Waves, Die Grundlagen der mathematischen Wissenschaften
– uller, C
- 1969
|
|
1
|
A Pyramid Scheme for Spherical Wavelets, AGTM-Report 170
– Schreiner
- 1996
|
|
1
|
The Approximation of Harmonic Functions by Harmonic Polynomials and by Harmonic Rational Functions
– Walsh
- 1929
|
|
1
|
Approximation by Polynomials: Uniform Convergence as Implied by Mean Convergence
– Walsh
- 1966
|
