Biorthogonal Locally Supported Wavelets on the Sphere Based on Zonal Kernel Functions

  • This paper presents a method for approximating spherical functions from discrete data of a block-wise grid structure. The essential ingredients of the approach are scaling and wavelet functions within a biorthogonalisation process generated by locally supported zonal kernel functions. In consequence, geophysically and geodetically relevant problems involving rotation-invariant pseudodifferential operators become attackable. A multiresolution analysis is formulated enabling a fast wavelet transform similar to the algorithms known from one-dimensional Euclidean theory.

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Author:Willi Freeden, Michael Schreiner
URN (permanent link):urn:nbn:de:hbz:386-kluedo-14518
Serie (Series number):Schriften zur Funktionalanalysis und Geomathematik (27)
Document Type:Preprint
Language of publication:English
Year of Completion:2006
Year of Publication:2006
Publishing Institute:Technische Universität Kaiserslautern
Creating Corporation:AG Geomathematik
Date of the Publication (Server):2006/10/24
Tag:Biorthogonalisation; Decomposition and Reconstruction Schemes; Fast Wavelet Transform; Spherical Multiresolution Analysis; Zonal Kernel Functions
Faculties / Organisational entities:Fachbereich Mathematik
DDC-Cassification:5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik
MSC-Classification (mathematics):42-XX FOURIER ANALYSIS / 42Cxx Nontrigonometric harmonic analysis / 42C40 Wavelets and other special systems
43-XX ABSTRACT HARMONIC ANALYSIS (For other analysis on topological and Lie groups, see 22Exx) / 43Axx Abstract harmonic analysis / 43A90 Spherical functions [See also 22E45, 22E46, 33C55]
65-XX NUMERICAL ANALYSIS / 65Txx Numerical methods in Fourier analysis / 65T60 Wavelets
Licence (German):Standard gemäß KLUEDO-Leitlinien vor dem 27.05.2011

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