Geodesic
Tiling and spectral properties of near-cubic domains
Mihail N. Kolountzakis1 ; Izabella /Laba2
1Department of Mathematics University of Crete Knossos Ave. 714 09 Iraklio, Greece
2Department of Mathematics University of British Columbia Vancouver, B.C. V6T 1Z2, Canada
Studia Mathematica, Tome 160 (2004) no. 3, pp. 287-299
Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

Voir la notice de l'article

We prove that if a measurable domain tiles ${\mathbb R}$ or ${\mathbb R}^2$ by translations, and if it is “close enough” to a line segment or a square respectively, then it admits a lattice tiling. We also prove a similar result for spectral sets in dimension 1, and give an example showing that there is no analogue of the tiling result in dimensions 3 and higher.
DOI : 10.4064/sm160-3-6
Keywords: prove measurable domain tiles mathbb mathbb translations close enough line segment square respectively admits lattice tiling prove similar result spectral sets dimension example showing there analogue tiling result dimensions higher

Mihail N. Kolountzakis  1   ; Izabella /Laba  2

1 Department of Mathematics University of Crete Knossos Ave. 714 09 Iraklio, Greece
2 Department of Mathematics University of British Columbia Vancouver, B.C. V6T 1Z2, Canada 
@article{10_4064_sm160_3_6,
     author = {Mihail N. Kolountzakis and Izabella /Laba},
     title = {Tiling and spectral properties of
 near-cubic domains},
     journal = {Studia Mathematica},
     pages = {287--299},
     year = {2004},
     volume = {160},
     number = {3},
     doi = {10.4064/sm160-3-6},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/sm160-3-6/}
}
TY  - JOUR
AU  - Mihail N. Kolountzakis
AU  - Izabella /Laba
TI  - Tiling and spectral properties of
 near-cubic domains
JO  - Studia Mathematica
PY  - 2004
SP  - 287
EP  - 299
VL  - 160
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.4064/sm160-3-6/
DO  - 10.4064/sm160-3-6
LA  - en
ID  - 10_4064_sm160_3_6
ER  - 
%0 Journal Article
%A Mihail N. Kolountzakis
%A Izabella /Laba
%T Tiling and spectral properties of
 near-cubic domains
%J Studia Mathematica
%D 2004
%P 287-299
%V 160
%N 3
%U http://geodesic.mathdoc.fr/articles/10.4064/sm160-3-6/
%R 10.4064/sm160-3-6
%G en
%F 10_4064_sm160_3_6
Mihail N. Kolountzakis; Izabella /Laba. Tiling and spectral properties of
 near-cubic domains. Studia Mathematica, Tome 160 (2004) no. 3, pp. 287-299. doi: 10.4064/sm160-3-6

Cité par Sources :