UNIVERSITY OF CRETE
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DEPARTMENT OF MATHEMATICS
Knossos Ave., GR 714 09 Iraklio, Crete, Greece, Tel: +30 2810393800, Fax: +30 2810393881
In this talk 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.