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Locally Supported Wavelets on the Sphere
Author(s) -
Göttelmann Jochen
Publication year - 1998
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.19980781532
Subject(s) - wavelet , legendre wavelet , wavelet transform , basis (linear algebra) , sobolev space , construct (python library) , mathematics , lifting scheme , singularity , fast wavelet transform , discrete wavelet transform , computer science , mathematical analysis , gabor wavelet , pure mathematics , algorithm , artificial intelligence , geometry , programming language
We construct explicitly wavelets on the sphere that provide a locally supported and stable basis for the Sobolev spaces H 2 ,0 ⩽ s < 1. We get at hand at fast wavelet transform with almost optimal complexity. This basis can be easily implemented in numerical schemes. We apply the wavelet transform to singularity detection and data compression. This contribution summarizes the results of [1].