Fourier frequencies in affine iterated function systems
| dc.creator | Dutkay, Dorin E. | |
| dc.creator | Jorgensen, Palle E. T. | |
| dc.date | 2006-04-25 | |
| dc.date | 2006-10-06 | |
| dc.date.accessioned | 2026-07-07T08:38:12Z | |
| dc.date.available | 2026-07-07T08:38:12Z | |
| dc.description | We examine two questions regarding Fourier frequencies for a class of iterated function systems (IFS). These are iteration limits arising from a fixed finite families of affine and contractive mappings in $\br^d$, and the ``IFS'' refers to such a finite system of transformations, or functions. The iteration limits are pairs $(X, μ)$ where $X$ is a compact subset of $\br^d$, (the support of $μ$) and the measure $μ$ is a probability measure determined uniquely by the initial IFS mappings, and a certain strong invariance axiom. The two questions we study are: (1) existence of an orthogonal Fourier basis in the Hilbert space $L^2(X,μ)$; and (2) the interplay between the geometry of $(X, μ)$ on the one side, and the spectral data entailed by possible Fourier bases. | |
| dc.description | new version, we included the suggestions of the referee | |
| dc.identifier | https://arxiv.org/abs/math/0604547 | |
| dc.identifier | http://arxiv.org/abs/math/0604547 | |
| dc.identifier | J. Funct. Anal. 247 (2007), no. 1, 110--137 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/140645 | |
| dc.subject | Functional Analysis | |
| dc.subject | Spectral Theory | |
| dc.subject | 28A80, 42B05, 60G42, 46C99, 44.30, 37B25, 47A10 | |
| dc.title | Fourier frequencies in affine iterated function systems | |
| dc.type | text |