An example concerning Fourier analytic criteria for translational tiling

N Lev

doi:10.4171/rmi/1318

An example concerning Fourier analytic criteria for translational tiling

N Lev

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

It is well known that the functions f ∊ L¹(R^d) whose translates along a lattice Λ form a tiling, can be completely characterized in terms of the zero set of their Fourier transform. We construct an example of a discrete set Λ ⊂ R (a small perturbation of the integers) for which no characterization of this kind is possible: there are two functions f; g ∊ L¹(R) whose Fourier transforms have the same set of zeros, but such that f + Λ is a tiling while g + Λ is not.

Original language	American English
Pages (from-to)	1975-1991
Number of pages	17
Journal	Revista Matematica Iberoamericana
Volume	38
Issue number	6
DOIs	https://doi.org/10.4171/rmi/1318
State	Published - 2022

Bibliographical note

Funding Information:
Funding. Research supported by ISF Grant No. 227/17 and ERC Starting Grant No. 713927.

Publisher Copyright:
© 2021 Real Sociedad Matemática Española Published by EMS Press.

Keywords

Fourier transform
Tiling
Distributions
Spectral synthesis
Translates

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KW - Fourier transform

KW - Tiling

KW - Distributions

KW - Spectral synthesis

KW - Translates

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An example concerning Fourier analytic criteria for translational tiling

Abstract

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Keywords

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