Generalized multiresolution analyses with given multiplicity functions
| dc.creator | Baggett, Lawrence W. | |
| dc.creator | Larsen, Nadia S. | |
| dc.creator | Merrill, Kathy D. | |
| dc.creator | Packer, Judith A. | |
| dc.creator | Raeburn, Iain | |
| dc.date | 2007-10-10 | |
| dc.date.accessioned | 2026-07-07T08:35:31Z | |
| dc.date.available | 2026-07-07T08:35:31Z | |
| dc.description | Generalized multiresolution analyses are increasing sequences of subspaces of a Hilbert space $\H$ that fail to be multiresolution analyses in the sense of wavelet theory because the core subspace does not have an orthonormal basis generated by a fixed scaling function. Previous authors have studied a multiplicity function $m$ which, loosely speaking, measures the failure of the GMRA to be an MRA. When the Hilbert space $\H$ is $L^2(\mathbb R^n)$, the possible multiplicity functions have been characterized by Baggett and Merrill. Here we start with a function $m$ satisfying a consistency condition which is known to be necessary, and build a GMRA in an abstract Hilbert space with multiplicity function $m$. | |
| dc.description | 16 pages including bibliography | |
| dc.identifier | https://arxiv.org/abs/0710.2071 | |
| dc.identifier | http://arxiv.org/abs/0710.2071 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/139769 | |
| dc.subject | Functional Analysis | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | 42C40; 47D03 | |
| dc.title | Generalized multiresolution analyses with given multiplicity functions | |
| dc.type | text |