Accuracy, Sum Rules and Crystal Wavelets

MOLTER, URSULA

Nashville

Congreso; 5th International Conference on Computational Harmonic Analysis in conjunction with the 29th annual Shanks Lecture; 2014

Vanderbilt University

The scaling function of a crystal Multiresolution Analysis can be identified with a vector-scaling function for a Multiresolution Analysis associated to a lattice. Therefore, the well known techniques for this case can be applied. (Eg: determining the accuracy, approximation properties, etc.) However, the structure that the underlying crystal group provides, enables us to simplify these properties - and for example allows to find sum rules for multiwavelets, which before were only available for single functions. The group structure is also helpful for the actual construction of crystal scaling functions. Further, when trying to build the crystal wavelet basis, much fewer calculations have to be performed by taking advantage of the tight structure imposed by the crystal group.