m at h . FA ] 1 6 Fe b 20 00 Wavelet filters and infinite - dimensional unitary groups

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 ON . 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.