On the construction of multivariate (pre)wavelets

A new approach for the construction of wavelets and prewavelets onRd from multiresolution is presented. The method uses only properties of shift-invariant spaces and orthogonal projectors fromL2(Rd) onto these spaces, and requires neither decay nor stability of the scaling function. Furthermore, this approach allows a simple derivation of previous, as well as new, constructions of wavelets, and leads to a complete resolution of questions concerning the nature of the intersection and the union of a scale of spaces to be used in a multiresolution.

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