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
Tag:Biorthogonalisation; Decomposition and Reconstruction Schemes; Fast Wavelet Transform; Spherical Multiresolution Analysis; Zonal Kernel Functions
Faculties / Organisational entities:Fachbereich Mathematik
DDC-Cassification:510 Mathematik
MSC-Classification (mathematics):42C40 Wavelets and other special systems
43A90 Spherical functions [See also 22E45, 22E46, 33C55]
65T60 Wavelets

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