Revista Matemática Iberoamericana

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Volume 12, Issue 1, 1996, pp. 1–18
DOI: 10.4171/RMI/191

Published online: 1996-04-30

Wavelets obtained by continuous deformations of the Haar wavelet

Aline Bonami[1], Sylvain Durand[2] and Guido Weiss[3]

(1) Université d'Orléans, France
(2) Université d'Orléans, Orléans, France
(3) Washington University in St. Louis, USA

One might obtain the impression, from the wavelet literature, that the class of orthogonal wavelets is divided into subclasses, like compactly supported ones on one side, band-limited ones on the other side. The main purpose of this work is to show that, in fact, the class of low-pass filters associated with "reasonable" (in the localization sense, not necessarily in the smooth sense) wavelets can be considered to be an infinite dimensional manifold that is arcwise connected. In particular, we show that any such wavelet can be connected in this way to the Haar wavelet.

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Bonami Aline, Durand Sylvain, Weiss Guido: Wavelets obtained by continuous deformations of the Haar wavelet. Rev. Mat. Iberoamericana 12 (1996), 1-18. doi: 10.4171/RMI/191