Wavelets obtained by continuous deformations of the Haar wavelet (Q1914385)

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.