Abstract
We shall describe a way to construct wavelets on an open set Ω of Rn (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 Rn) and the fast decomposition algorithms (which are of a similar kind as in Rn except that the storage of more filters is needed).
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Bibliography
S. Jaffard et Y. Meyer, Bases d’ondelettes dans des ouverts de Rn to appear in Journal des Mathématiques pures et appliquées
S. Mallat, A theory for multiresolution signal decomposition: The wavelet representation. Dept of computer science, University of Pennsylvania, PA 19104–6389,USA
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© 1990 Springer-Verlag Berlin Heidelberg
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Jaffard, S. (1990). Construction of Wavelets on Open Sets. In: Combes, JM., Grossmann, A., Tchamitchian, P. (eds) Wavelets. inverse problems and theoretical imaging. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-75988-8_23
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DOI: https://doi.org/10.1007/978-3-642-75988-8_23
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-53014-5
Online ISBN: 978-3-642-75988-8
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