Isometries, shifts, Cuntz algebras and multiresolution wavelet analysis of scale N
| dc.creator | Bratteli, Ola | |
| dc.creator | Jorgensen, Palle E. T. | |
| dc.date | 1996-12-17 | |
| dc.date.accessioned | 2026-07-07T09:13:40Z | |
| dc.date.available | 2026-07-07T09:13:40Z | |
| dc.description | In this paper we show how wavelets originating from multiresolution analysis of scale N give rise to certain representations of the Cuntz algebras O_N, and conversely how the wavelets can be recovered from these representations. The representations are given on the Hilbert space L^2(T) by (S_iξ)(z)=m_i(z)ξ(z^N). We characterize the Wold decomposition of such operators. If the operators come from wavelets they are shifts, and this can be used to realize the representation on a certain Hardy space over L^2(T). This is used to compare the usual scale-2 theory of wavelets with the scale-N theory. Also some other representations of O_N of the above form called diagonal representations are characterized and classified up to unitary equivalence by a homological invariant. | |
| dc.description | 59 pages, AMS-LaTeX v1.2b | |
| dc.identifier | https://arxiv.org/abs/funct-an/9612003 | |
| dc.identifier | http://arxiv.org/abs/funct-an/9612003 | |
| dc.identifier | Integral Equations and Operator Theory 28 (1997), no. 4, 382--443 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/152406 | |
| dc.subject | Functional Analysis | |
| dc.subject | Operator Algebras | |
| dc.subject | 46L55, 47C15 (Primary) 42C05, 22D25, 11B85 (Secondary) | |
| dc.title | Isometries, shifts, Cuntz algebras and multiresolution wavelet analysis of scale N | |
| dc.type | text |