Construction of Multivariate (pre) Wavelets.

摘要

A new approach for the construction of wavelets and prewavelets on IR d from multiresolution is presented. The method uses only properties of shift-invariant spaces and orthogonal projectors from L2(IRd) 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. wavelets, multiresolution, shift-invariant spaces, box splines.