Geodesic
Tiling by translates of a function: results and open problems
Discrete analysis (2021)
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We say that a function $f \in L^1(\mathbb{R})$ tiles at level $w$ by a discrete translation set $Λ\subset \mathbb{R}$, if we have $\sum_{λ\in Λ} f(x-λ)=w$ a.e. In this paper we survey the main results, and prove several new ones, on the structure of tilings of $\mathbb{R}$ 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.
Publié le : 
@article{DAS_2021_a15,
     author = {Mihail N. Kolountzakis and Nir Lev},
     title = {Tiling by translates of a function: results and open problems},
     journal = {Discrete analysis},
     year = {2021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DAS_2021_a15/}
}
TY  - JOUR
AU  - Mihail N. Kolountzakis
AU  - Nir Lev
TI  - Tiling by translates of a function: results and open problems
JO  - Discrete analysis
PY  - 2021
UR  - http://geodesic.mathdoc.fr/item/DAS_2021_a15/
LA  - en
ID  - DAS_2021_a15
ER  - 
%0 Journal Article
%A Mihail N. Kolountzakis
%A Nir Lev
%T Tiling by translates of a function: results and open problems
%J Discrete analysis
%D 2021
%U http://geodesic.mathdoc.fr/item/DAS_2021_a15/
%G en
%F DAS_2021_a15
Mihail N. Kolountzakis; Nir Lev. Tiling by translates of a function: results and open problems. Discrete analysis (2021). http://geodesic.mathdoc.fr/item/DAS_2021_a15/