Functions tiling with several lattices

2021/06/22 by Kolountzakis, Mihail N., Papageorgiou, Effie · 4 citations
#Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.2106.11701

Abstract

We study the problem of finding a function f with ``small support'' that simultaneously tiles with finitely many lattices Λ₁, …, Λ_N in d-dimensional Euclidean spaces. We prove several results, both upper bounds (constructions) and lower bounds on how large this support can and must be. We also study the problem in the setting of finite abelian groups, which turns out to be the most concrete setting. Several open questions are posed.

Cited by

• Bounded lattice tiles that pack with another lattice
• Are MSF wavelets minimally supported?
• Bounded common fundamental domains for two lattices
• Strictly Expansive Matrices

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