Spectra for cubes in products of finite cyclic groups
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- by Elona Agora, Sigrid Grepstad and Mihail N. Kolountzakis PDF
- Proc. Amer. Math. Soc. 146 (2018), 2417-2423 Request permission
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.References
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Additional Information
- Elona Agora
- Affiliation: Instituto Argentino de Matemática “Alberto P. Calderón” (IAM-CONICET), Argentina
- MR Author ID: 983593
- 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
- MR Author ID: 1047019
- 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
- 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
- © Copyright 2018 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 146 (2018), 2417-2423
- MSC (2010): Primary 42B05, 52C22
- DOI: https://doi.org/10.1090/proc/14017
- MathSciNet review: 3778145