00-439 Ola Bratteli, Palle E.T. Jorgensen

Wavelet filters and infinite-dimensional unitary groups (118K, LaTeX2e amsproc class, 30 pages) Nov 8, 00

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Abstract. 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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