# A class of non-convex polytopes that admit no orthonormal basis of exponentials

@article{Kolountzakis2001ACO, title={A class of non-convex polytopes that admit no orthonormal basis of exponentials}, author={Mihail N. Kolountzakis and Michael Papadimitrakis}, journal={Illinois Journal of Mathematics}, year={2001}, volume={46}, pages={1227-1232} }

A conjecture of Fuglede states that a bounded measurable set ⊂ R d , of measure 1, can tile R d by translations if and only if the Hilbert space L 2 () has an orthonormal basis consisting of exponentials e�(x) = exp 2πih λ, xi . If has the latter property it is called spectral. Let be a polytope in R d with the following property: there is a direction ξ ∈ S d 1 such that, of all the polytope faces perpendicular to ξ, the total area of the faces pointing in the positive ξ direction is more than… Expand

#### 11 Citations

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Spectrality of Polytopes and Equidecomposability by Translations

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