Coxeter Groups and Wavelet Sets

Details Coxeter Groups and Wavelet Sets Coxeter Groups and Wavelet Sets

2007-10-19

arxiv.org/abs/0710.3655v1

Mathematics

Functional Analysis

Scientific paper

A traditional wavelet is a special case of a vector in a separable Hilbert space that generates a basis under the action of a system of unitary operators defined in terms of translation and dilation operations. A Coxeter/fractal-surface wavelet is obtained by defining fractal surfaces on foldable figures, which tesselate the embedding space by reflections in their bounding hyperplanes instead of by translations along a lattice. Although both theories look different at their onset, there exist connections and communalities which are exhibited in this semi-expository paper. In particular, there is a natural notion of a dilation-reflection wavelet set. We prove that dilation-reflection wavelet sets exist for arbitrary expansive matrix dilations, paralleling the traditional dilation-translation wavelet theory. There are certain measurable sets which can serve simultaneously as dilation-translation wavelet sets and dilation-reflection wavelet sets, although the orthonormal structures generated in the two theories are considerably different.

Affiliated with

Also associated with

No associations

Rating

Coxeter Groups and Wavelet Sets does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Coxeter Groups and Wavelet Sets, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Coxeter Groups and Wavelet Sets will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-708414