Universal Spectra and Tijdeman's Conjecture on Factorization of Cyclic Groups
| dc.creator | Lagarias, Jeffrey C. | |
| dc.creator | Szabo, Sandor | |
| dc.date | 2000-08-16 | |
| dc.date.accessioned | 2026-07-07T04:36:51Z | |
| dc.date.available | 2026-07-07T04:36:51Z | |
| dc.description | A spectral set in R^n is a set X of finite Lebesgue measure such that L^2(X) has an orthogonal basis of exponentials. It is conjectured that every spectral set tiles R^n by translations. A set of translations T has a universal spectrum if every set that that tiles by translations by T has this spectrum. A recent result proved that many periodic tiling sets have universal spectra, using results from factorizations of abelian groups, for groups for which a strong form of a conjecture of Tijdeman is valid. This paper shows Tijdeman's conjecture does not hold for the cyclic group of order 900. It formulates a new sufficient conjecture for a periodic tiling set to have a universal spectrum, and uses it to show that the tiling sets for the counterexample above do have universal spectra. | |
| dc.description | 9 pages, latex, to appear J. Fourier Anal. Appl | |
| dc.identifier | https://arxiv.org/abs/math/0008132 | |
| dc.identifier | http://arxiv.org/abs/math/0008132 | |
| dc.identifier | J. Fourier Anal. Appl. 7 (2001), 63--70. | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/59752 | |
| dc.subject | Functional Analysis | |
| dc.subject | Spectral Theory | |
| dc.subject | Primary: 47A13 Secondary: 11K70, 42B05 | |
| dc.title | Universal Spectra and Tijdeman's Conjecture on Factorization of Cyclic Groups | |
| dc.type | text |