Banach frames for alpha-modulation spaces
| dc.creator | Fornasier, Massimo | |
| dc.date | 2004-10-26 | |
| dc.date.accessioned | 2026-07-07T05:13:42Z | |
| dc.date.available | 2026-07-07T05:13:42Z | |
| dc.description | This paper is concerned with the characterization of $α$-modulation spaces by Banach frames, i.e., stable and redundant non-orthogonal expansions, constituted of functions obtained by a suitable combination of translation, modulation and dilation of a mother atom. In particular, the parameter $α\in [0,1]$ governs the dependence of the dilation factor on the frequency. The result is achieved by exploiting intrinsic properties of localization of such frames. The well-known Gabor and wavelet frames arise as special cases ($α= 0$) and limiting case ($ α\to 1)$, to characterize respectively modulation and Besov spaces. This intermediate theory contributes to a further answer to the theoretical need of a common interpretation and framework between Gabor and wavelet theory and to the construction of new tools for applications in time-frequency analysis, signal processing, and numerical analysis. | |
| dc.description | 24 pages, 1 figure | |
| dc.identifier | https://arxiv.org/abs/math/0410549 | |
| dc.identifier | http://arxiv.org/abs/math/0410549 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/73009 | |
| dc.subject | Functional Analysis | |
| dc.subject | 42B35, 42C15, 46B25, 65T60 | |
| dc.title | Banach frames for alpha-modulation spaces | |
| dc.type | text |