Tiling and weak tiling in [Formula: see text]

We discuss the relation of tiling, weak tiling and spectral sets in finite abelian groups. In particular, in elementary p-groups [Formula: see text] , 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...

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Autores principales: Kiss, Gergely, Matolcsi, Dávid, Matolcsi, Máté, Somlai, Gábor
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer International Publishing 2023
Materias:
Original Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10695897/
http://dx.doi.org/10.1007/s43670-023-00073-7
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author Kiss, Gergely
Matolcsi, Dávid
Matolcsi, Máté
Somlai, Gábor
author_facet Kiss, Gergely
Matolcsi, Dávid
Matolcsi, Máté
Somlai, Gábor
author_sort Kiss, Gergely
collection PubMed
description We discuss the relation of tiling, weak tiling and spectral sets in finite abelian groups. In particular, in elementary p-groups [Formula: see text] , 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 [Formula: see text] , and prove some partial results for [Formula: see text] .
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spelling pubmed-106958972023-12-06 Tiling and weak tiling in [Formula: see text] Kiss, Gergely Matolcsi, Dávid Matolcsi, Máté Somlai, Gábor Sampl Theory Signal Process Data Anal Original Article We discuss the relation of tiling, weak tiling and spectral sets in finite abelian groups. In particular, in elementary p-groups [Formula: see text] , 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 [Formula: see text] , and prove some partial results for [Formula: see text] . Springer International Publishing 2023-12-04 2024 /pmc/articles/PMC10695897/ http://dx.doi.org/10.1007/s43670-023-00073-7 Text en © The Author(s) 2023 https://creativecommons.org/licenses/by/4.0/Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/ (https://creativecommons.org/licenses/by/4.0/) .
spellingShingle Original Article
Kiss, Gergely
Matolcsi, Dávid
Matolcsi, Máté
Somlai, Gábor
Tiling and weak tiling in [Formula: see text]
title Tiling and weak tiling in [Formula: see text]
title_full Tiling and weak tiling in [Formula: see text]
title_fullStr Tiling and weak tiling in [Formula: see text]
title_full_unstemmed Tiling and weak tiling in [Formula: see text]
title_short Tiling and weak tiling in [Formula: see text]
title_sort tiling and weak tiling in [formula: see text]
topic Original Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10695897/
http://dx.doi.org/10.1007/s43670-023-00073-7
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