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 |
Keywords
- Quasicrystals
- Spectral gap
- Tiling
- Translates
- Uncertainty principle
All Science Journal Classification (ASJC) codes
- Algebra and Number Theory
- Geometry and Topology
- Discrete Mathematics and Combinatorics
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