Construction of Parseval wavelets from redundant filter systems
| dc.creator | Baggett, L. W. | |
| dc.creator | Jorgensen, P. E. T. | |
| dc.creator | Merrill, K. D. | |
| dc.creator | Packer, J. A. | |
| dc.date | 2004-05-14 | |
| dc.date | 2005-05-05 | |
| dc.date.accessioned | 2026-07-07T06:21:35Z | |
| dc.date.available | 2026-07-07T06:21:35Z | |
| dc.description | We consider wavelets in L^2(R^d) which have generalized multiresolutions. This means that the initial resolution subspace V_0 in L^2(R^d) is not singly generated. As a result, the representation of the integer lattice Z^d restricted to V_0 has a nontrivial multiplicity function. We show how the corresponding analysis and synthesis for these wavelets can be understood in terms of unitary-matrix-valued functions on a torus acting on a certain vector bundle. Specifically, we show how the wavelet functions on R^d can be constructed directly from the generalized wavelet filters. | |
| dc.description | 34 pages, AMS-LaTeX ("amsproc" document class) v2 changes minor typos in Sections 1 and 4, v3 adds a number of references on GMRA theory and wavelet multiplicity analysis; v4 adds material on pages 2, 3, 5 and 10, and two more references | |
| dc.identifier | https://arxiv.org/abs/math/0405301 | |
| dc.identifier | http://arxiv.org/abs/math/0405301 | |
| dc.identifier | doi:10.1063/1.1982768 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/95645 | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | Operator Algebras | |
| dc.subject | Primary 54C40, 14E20, 42A65; Secondary 46E25, 20C20 | |
| dc.title | Construction of Parseval wavelets from redundant filter systems | |
| dc.type | text |