Wavelet filters and infinite-dimensional unitary groups

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dc.creatorBratteli, Ola
dc.creatorJorgensen, Palle E. T.
dc.date2000-01-28
dc.date2000-08-14
dc.date.accessioned2026-07-07T04:33:29Z
dc.date.available2026-07-07T04:33:29Z
dc.descriptionIn 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.
dc.descriptionAMS-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
dc.identifierhttps://arxiv.org/abs/math/0001171
dc.identifierhttp://arxiv.org/abs/math/0001171
dc.identifierWavelet Analysis and Applications (Guangzhou, China, 1999) (Donggao Deng, Daren Huang, Rong-Qing Jia, Wei Lin, and Jianzhong Wang, eds., catalogued under Deng alone), AMS/IP Studies in Advanced Mathematics, vol. 25, American Mathematical Society, Providence, International Press, 2002, pp. 35--65
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/58592
dc.subjectFunctional Analysis
dc.subject46L60, 47D25, 42A16, 43A65 (Primary), 46L45, 42A65, 41A15 (Secondary)
dc.titleWavelet filters and infinite-dimensional unitary groups
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