Fuglede's conjecture fails in dimension 4

Author:
Máté Matolcsi

Journal:
Proc. Amer. Math. Soc. **133** (2005), 3021-3026

MSC (2000):
Primary 42B99; Secondary 20K01

Published electronically:
March 24, 2005

MathSciNet review:
2159781

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: In this note we modify a recent example of Tao and give an example of a set such that admits an orthonormal basis of exponentials for some set , but which does not tile 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.

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Additional Information

**Máté Matolcsi**

Affiliation:
Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences, POB 127 H-1364 Budapest, Hungary

Email:
matomate@renyi.hu

DOI:
http://dx.doi.org/10.1090/S0002-9939-05-07874-3

Keywords:
Translational tiles,
spectral sets,
Fuglede's conjecture,
Hadamard matrices

Received by editor(s):
May 21, 2004

Published electronically:
March 24, 2005

Additional Notes:
The author was supported by Hungarian Research Funds OTKA-T047276, OTKA-F049457, OTKA-T049301

Communicated by:
Andreas Seeger

Article copyright:
© Copyright 2005
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.