ON THE CONSTRUCTION OF MULTIVARIATE (PRE)WAVELETS

A new approach for the construction of wavelets and prewavelets on R(d) from multiresolution is presented. The method uses only properties of shift-invariant spaces and orthogonal projectors from L2(R(d)) 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 multi-resolution.