# Tiling sets and spectral sets over finite fields

@article{Aten2015TilingSA,
title={Tiling sets and spectral sets over finite fields},
author={Charlotte Aten and B. Ayachi and E. Bau and D. Fitzpatrick and Alex Iosevich and H. X. Liu and Adam Lott and I. Mackinnon and Shir Maimon and S. Nan and Jonathan Pakianathan and Giorgis Petridis and C. Rojas Mena and A. Sheikh and Tim Tribone and Jean-Christophe Weill and C. Yu},
journal={arXiv: Classical Analysis and ODEs},
year={2015}
}
• Published 3 September 2015
• Mathematics
• arXiv: Classical Analysis and ODEs

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Abstract We exhibit a subset of a finite Abelian group, which tiles the group by translation, and such that its tiling complements do not have a common spectrum (orthogonal basis for their L 2 space

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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