Tiling and weak tiling in $$(\mathbb {Z}_p)^d$$
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Published:2023-12-04
Issue:1
Volume:22
Page:
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ISSN:2730-5716
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Container-title:Sampling Theory, Signal Processing, and Data Analysis
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language:en
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Short-container-title:Sampl. Theory Signal Process. Data Anal.
Author:
Kiss Gergely, Matolcsi Dávid, Matolcsi MátéORCID, Somlai Gábor
Abstract
AbstractWe discuss the relation of tiling, weak tiling and spectral sets in finite abelian groups. In particular, in elementary p-groups $$(\mathbb {Z}_p)^d$$
(
Z
p
)
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 $$d=1, 2$$
d
=
1
,
2
, and prove some partial results for $$d=3$$
d
=
3
.
Funder
NKFIH Magyar Tudományos Akadèmia UNKP European Research Council Budapest University of Technology and Economics
Publisher
Springer Science and Business Media LLC
Subject
Computational Mathematics,Radiology, Nuclear Medicine and imaging,Signal Processing,Algebra and Number Theory,Analysis
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1 articles.
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