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Wavelets obtained by continuous deformations of the Haar wavelet. (English) Zbl 0892.42020

Summary: 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.

MSC:

42C40 Nontrigonometric harmonic analysis involving wavelets and other special systems
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