JournalsrmiVol. 12, No. 1pp. 1–18

Wavelets obtained by continuous deformations of the Haar wavelet

  • Aline Bonami

    Université d'Orléans, France
  • Sylvain Durand

    Université d'Orléans, Orléans, France
  • Guido Weiss

    Washington University in St. Louis, USA
Wavelets obtained by continuous deformations of the Haar wavelet cover
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Abstract

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.

Cite this article

Aline Bonami, Sylvain Durand, Guido Weiss, Wavelets obtained by continuous deformations of the Haar wavelet. Rev. Mat. Iberoam. 12 (1996), no. 1, pp. 1–18

DOI 10.4171/RMI/191