Kiss, Gergely and Matolcsi, Dávid and Matolcsi, Máté and Somlai, Gábor (2024) Tiling and Weak Tiling in (Zp)d. SAMPLING THEORY, SIGNAL PROCESSING, AND DATA ANALYSIS, 22 (1). No.-1. ISSN 2730-5716 (print); 2730-5724 (online)
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Official URL: https://doi.org/10.1007/s43670-023-00073-7
Abstract
We discuss the relation of tiling, weak tiling and spectral sets in finite abelian groups. In particular, in elementary p -groups (Zp)d, we introduce an averaging procedure that leads to a natural object of study: a 4-tuple of functions which can be regarded as a common generalization of tiles and spectral sets. We characterize such 4-tuples for d=1,2 and prove some partial results for d=3.
| Item Type: | Article |
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| Uncontrolled Keywords: | Fuglede’s conjecture, Translational tiles, Spectral sets, Weak tiling, Abelian p-groups |
| Subjects: | Q Science / természettudomány > QA Mathematics / matematika |
| SWORD Depositor: | MTMT SWORD |
| Depositing User: | MTMT SWORD |
| Date Deposited: | 30 Jan 2024 09:23 |
| Last Modified: | 30 Jan 2024 09:23 |
| URI: | http://real.mtak.hu/id/eprint/186638 |
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