Compactly supported wavelets and representations of the Cuntz relations

Details Compactly supported wavelets and representations of the Cuntz relations Compactly supported wavelets and representations of the Cuntz relations

1999-12-15

arxiv.org/abs/math/9912129v1

Applied and Computational Harmonic Analysis 8 (2000), 166--196.

Mathematics

Functional Analysis

AMS-LaTeX; 29 pages, 6 figures incorporating 23 EPS diagrams and 1 LaTeX picture

Scientific paper

10.1006/acha.2000.0283

We study the harmonic analysis of the quadrature mirror filters coming from multiresolution wavelet analysis of compactly supported wavelets. It is known that those of these wavelets that come from third order polynomials are parametrized by the circle, and we compute that the corresponding filters generate irreducible mutually disjoint representations of of the Cuntz algebra $ O_{2} $ except at two points on the circle. One of the two exceptional points corresponds to the Haar wavelet and the other is the unique point on the circle where the father function defines a tight frame which is not an orthonormal basis. At these two points the representation decomposes into two and three mutually disjoint irreducible representations, respectively, and the two representations at the Haar point are each unitarily equivalent to one of the three representations at the other singular point.

Affiliated with

Also associated with

No associations

Rating

Compactly supported wavelets and representations of the Cuntz relations 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 Compactly supported wavelets and representations of the Cuntz relations, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Compactly supported wavelets and representations of the Cuntz relations will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-580931