Construction of Wavelets on Open Sets
We shall describe a way to construct wavelets on an open set Ω of R n (this construction is a joint work with Y.MEYER and can be found in (1) ;the reader should look there for precisions),then we shall give a more explicit description of the two following points that are important for possible applications: The asymptotic behavior (wavelets that are localized around very small cubes which are far from the boundary of Ω are numerically identical to the ”corresponding” wavelet on R n ) and the fast decomposition algorithms (which are of a similar kind as in R n except that the storage of more filters is needed).
KeywordsOrthonormal Basis Asymptotic Estimate Multiresolution Analysis Riesz Basis Unconditional Basis
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- 1.S. Jaffard et Y. Meyer, Bases d’ondelettes dans des ouverts de Rn to appear in Journal des Mathématiques pures et appliquéesGoogle Scholar
- 2.S. Mallat, A theory for multiresolution signal decomposition: The wavelet representation. Dept of computer science, University of Pennsylvania, PA 19104–6389,USAGoogle Scholar