Harmonic Analysis of Fractal Measures
| dc.creator | Jorgensen, Palle E. T. | |
| dc.creator | Pedersen, Steen | |
| dc.date | 2006-04-04 | |
| dc.date.accessioned | 2026-07-07T07:10:31Z | |
| dc.date.available | 2026-07-07T07:10:31Z | |
| dc.description | This paper introduces Fourier duality for a class of affine iterated function systems (IFS) T_i. These systems are determined by a finite family of contractive affine maps in R^d. Our Fourier duality applies to the resulting probability measure mu which is fixed by (T_i). When the IFS is given, the support of the associated mu is a compact set X in R^d, typically a fractal. Our Fourier duality refers to the Hilbert space L^2(X, mu): We show that under a certain unitarity condition involving a pair of affine iterated function systems (T_i) and (S_j) it is possible to recursively construct a Fourier bases in the Hilbert space L^2(X, mu) with the Fourier basis for one depending on the other. | |
| dc.description | 38 pages, AMS-TeX ("amsppt" document style) | |
| dc.identifier | https://arxiv.org/abs/math/0604087 | |
| dc.identifier | http://arxiv.org/abs/math/0604087 | |
| dc.identifier | Constr. Approx. 12 (1996), 1--30 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/111446 | |
| dc.subject | Functional Analysis | |
| dc.subject | 28A75, 42B10, 46L55 (Primary) 05B45 (Secondary) | |
| dc.title | Harmonic Analysis of Fractal Measures | |
| dc.type | text |