Wavelet filters and infinite-dimensional unitary groups

Details Wavelet filters and infinite-dimensional unitary groups Wavelet filters and infinite-dimensional unitary groups

2000-01-28

arxiv.org/abs/math/0001171v3

Wavelet Analysis and Applications (Guangzhou, China, 1999) (Donggao Deng, Daren Huang, Rong-Qing Jia, Wei Lin, and Jianzhong W

Mathematics

Functional Analysis

AMS-LaTeX; 30 pages, 2 tables, 1 picture. Invited lecture by Jorgensen at International Conference on Wavelet Analysis and Its

Scientific paper

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.

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