Computationally Efficient Wavelets in Sobolev Spaces

Rudolph A. Lorentz

GMD - German National Research Center for Information Technology
Schloß Birlinghoven
D-53754 Sankt Augustin
Germany


Abstract

We show that there do not exist any compactly supported prewavelets with respect to Sobolev seminorms for the multiresolution analysis generated by box splines in d-dimensional Euclidean space for d > 2. Neither do there exist compactly supported prewavelets with respect to the full norm, nor if we use one Sobolev norm to define the semiorthogonality and another for the Riesz basis property of the prewavelets.

The case d = 1 is an exception, since it is already known that compactly supported univariate spline prewavelets exist for integer s.

This is work done together with P. Oswald.