Abstract
It is well known that the functions f ∊ L1(Rd) 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 | English |
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Pages (from-to) | 1975-1991 |
Number of pages | 17 |
Journal | Revista Matematica Iberoamericana |
Volume | 38 |
Issue number | 6 |
DOIs | |
State | Published - 2022 |
Bibliographical note
Publisher Copyright:© 2021 Real Sociedad Matemática Española Published by EMS Press.
Funding
Funding. Research supported by ISF Grant No. 227/17 and ERC Starting Grant No. 713927.
Funders | Funder number |
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European Commission | 713927 |
Israel Science Foundation | 227/17 |
Keywords
- Fourier transform
- Tiling
- distributions
- spectral synthesis
- translates