BAND-LIMITED WAVELETS

This manuscript represents a series of lectures, a ''mini course,'' presented by Guido Weiss during the Conference in Harmonic Analysis and Partial Differential Equations that was held in Miraflores de la Sierra in June 1992. This presentation can be regarded as an introduction to ''wavelets'' and this material is, for the most part, self-contained. The lectures, however, are aimed at an audience that knows the fundamentals of Harmonic Analysis. We are considering those wavelets whose Fourier transforms are compactly supported since many of their properties are more easily formulated and derived than those of the more general wavelets. As is pointed out in the text, however, much of the material presented here is true more generally. Much of this development appears, perhaps in different form, elsewhere; nevertheless, we do introduce some new results. All this is carefully explained in the text.