Wavelet filters and infinite-dimensional unitary groups
摘要
In this paper, we study wavelet filters and their dependence on two numbers, the scale N and the genus g. We show that the wavelet filters, in the quadrature mirror case, have a harmonic analysis which is based on representations of the C^*-algebra O_N. A main tool in our analysis is the infinite-dimensional group of all maps T -> U(N) (where U(N) is the group of all unitary N-by-N matrices), and we study the extension problem from low-pass filter to multiresolution filter using this group.
引用
@article{arxiv.math/0001171,
title = {Wavelet filters and infinite-dimensional unitary groups},
author = {Ola Bratteli and Palle E. T. Jorgensen},
journal= {arXiv preprint arXiv:math/0001171},
year = {2007}
}
备注
AMS-LaTeX; 30 pages, 2 tables, 1 picture. Invited lecture by Jorgensen at International Conference on Wavelet Analysis and Its Applications, Zhongshan University, Guangzhou, China, in November 1999. Changes: Some references have been added and some technical points in several proofs have been clarified in this new revised version