Matolcsi, Máté (2005) Fuglede`s conjecture fails in dimension 4. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 133 (10). pp. 3021-3026. ISSN 0002-9939
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Official URL: http://www.ams.org/journals/proc/2005-133-10/S0002...
Abstract
In this note we modify a recent example of Tao and give an example of a set Omega subset of R-4 such that L-2(Omega) admits an orthonormal basis of exponentials {1/vertical bar Omega vertical bar 1/2 e(2 pi i < x,xi >)}(xi epsilon Lambda) for some set Lambda subset of R-4, but which does not tile R-4 by translations. This shows that one direction of Fuglede's conjecture fails already in dimension 4. Some common properties of translational tiles and spectral sets are also proved.
| Item Type: | Article |
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| Uncontrolled Keywords: | translational tiles; spectral sets; Hadamard Matrices; Fuglede's conjecture; BASES; DOMAINS; EXPONENTIALS |
| Subjects: | Q Science / természettudomány > QA Mathematics / matematika |
| SWORD Depositor: | MTMT SWORD |
| Depositing User: | MTMT SWORD |
| Date Deposited: | 10 Dec 2013 13:52 |
| Last Modified: | 10 Dec 2013 13:52 |
| URI: | http://real.mtak.hu/id/eprint/7952 |
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