Multiresolution Analysis by Spherical Up Functions

  • A new class of locally supported radial basis functions on the (unit) sphere is introduced by forming an infinite number of convolutions of ''isotropic finite elements''. The resulting up functions show useful properties: They are locally supported and are infinitely often differentiable. The main properties of these kernels are studied in detail. In particular, the development of a multiresolution analysis within the reference space of square--integrable functions over the sphere is given. Altogether, the paper presents a mathematically significant and numerically efficient introduction to multiscale approximation by locally supported radial basis functions on the sphere.

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Author:Willi Freeden, Michael Schreiner
URN (permanent link):urn:nbn:de:hbz:386-kluedo-12670
Serie (Series number):Schriften zur Funktionalanalysis und Geomathematik (2)
Document Type:Preprint
Language of publication:English
Year of Completion:2003
Year of Publication:2003
Publishing Institute:Technische Universität Kaiserslautern
Date of the Publication (Server):2003/11/10
Tag:Decomposition and Reconstruction Schemes; Multiresolution Analysis; Spherical Wavelets; Up Functions
Faculties / Organisational entities:Fachbereich Mathematik
DDC-Cassification:5 Naturwissenschaften und Mathematik / 510 Mathematik
Licence (German):Standard gemäß KLUEDO-Leitlinien vor dem 27.05.2011