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Spectra for cubes in products of finite cyclic groups


Authors: Elona Agora, Sigrid Grepstad and Mihail N. Kolountzakis
Journal: Proc. Amer. Math. Soc. 146 (2018), 2417-2423
MSC (2010): Primary 42B05, 52C22
DOI: https://doi.org/10.1090/proc/14017
Published electronically: February 21, 2018
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Abstract: We consider ``cubes'' in products of finite cyclic groups and we study their tiling and spectral properties. (A set in a finite group is called a tile if some of its translates form a partition of the group and is called spectral if it admits an orthogonal basis of characters for the functions supported on the set.) We show an analogue of a theorem due to Iosevich and Pedersen (1998), Lagarias, Reeds and Wang (2000), and the third author of this paper (2000), which identified the tiling complements of the unit cube in $ \mathbb{R}^d$ with the spectra of the same cube.


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Additional Information

Elona Agora
Affiliation: Instituto Argentino de Matemática “Alberto P. Calderón” (IAM-CONICET), Argentina
Email: elona.agora@gmail.com

Sigrid Grepstad
Affiliation: Institute of Financial Mathematics and Applied Number Theory, Johannes Kepler University Linz, Austria
Address at time of publication: Department of Mathematical Sciences, Norwegian University of Science and Technology, 7491 Trondheim, Norway
Email: sgrepstad@gmail.com

Mihail N. Kolountzakis
Affiliation: Department of Mathematics and Applied Mathematics, University of Crete, Voutes Campus, GR-700 13, Heraklion, Crete, Greece
Email: kolount@gmail.com

DOI: https://doi.org/10.1090/proc/14017
Received by editor(s): February 9, 2016
Published electronically: February 21, 2018
Additional Notes: This work has been partially supported by (1) the “Aristeia II” action (Project FOURIERDIG) of the operational program Education and Lifelong Learning (co-funded by the European Social Fund and Greek national resources) and (for the last author only) (2) by grant No 4725 of the University of Crete.
The first author has been partially supported by Grants: MTM2013-40985-P, MTM2016-75196-P, PIP No. 112201501003553CO, UBACyT 20020130100422BA
The second author was currently supported by the Austrian Science Fund (FWF), Project F5505-N26, which is a part of the Special Research Program “Quasi-Monte Carlo Methods: Theory and Applications”
Communicated by: Alexander Iosevich
Article copyright: © Copyright 2018 American Mathematical Society

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