## 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:nbn:de:hbz:386-kluedo-14518 Schriften zur Funktionalanalysis und Geomathematik (27) Preprint English 2006 2006 Technische Universität Kaiserslautern AG Geomathematik Biorthogonalisation; Decomposition and Reconstruction Schemes; Fast Wavelet Transform; Spherical Multiresolution Analysis; Zonal Kernel Functions Fachbereich Mathematik 510 Mathematik 42C40 Wavelets and other special systems 43A90 Spherical functions [See also 22E45, 22E46, 33C55] 65T60 Wavelets

$Rev: 12793$