Abstract
We say that a function (Formula Presented) tiles at level w by a discrete translation set ⋀⊂R, if we have (Formula Presented) In this paper we survey the main results, and prove several new ones, on the structure of tilings of R by translates of a function. The phenomena discussed include tilings of bounded and of unbounded density, uniform distribution of the translates, periodic and non-periodic tilings, and tilings at level zero. Fourier analysis plays an important role in the proofs. Some open problems are also given.
| Original language | English |
|---|---|
| Article number | 12 |
| Journal | Discrete Analysis |
| Volume | 2021 |
| DOIs | |
| State | Published - 2021 |
Bibliographical note
Publisher Copyright:© 2021. Mihail N. Kolountzakis and Nir Lev
Funding
*Supported by the Hellenic Foundation for Research and Innovation, Project HFRI-FM17-1733 and by Grant No. 4725 of the University of Crete. †Supported by ISF Grant No. 227/17 and ERC Starting Grant No. 713927.
| Funders | Funder number |
|---|---|
| European Commission | 713927 |
| Israel Science Foundation | 227/17 |
| University of Crete | |
| Hellenic Foundation for Research and Innovation | HFRI-FM17-1733, 4725 |
Keywords
- Quasicrystals
- Spectral gap
- Tiling
- Translates
- Uncertainty principle