Geodesic
On the Bragg Diffraction Spectra of a Meyer Set
Canadian journal of mathematics, Tome 65 (2013) no. 3, pp. 675-701

Voir la notice de l'article provenant de la source Cambridge

DOI

Meyer sets have a relatively dense set of Bragg peaks, and for this reason they may be considered as basic mathematical examples of (aperiodic) crystals. In this paper we investigate the pure point part of the diffraction of Meyer sets in more detail. The results are of two kinds. First, we show that, given a Meyer set and any positive intensity $a$ less than the maximum intensity of its Bragg peaks, the set of Bragg peaks whose intensity exceeds $a$ is itself a Meyer set (in the Fourier space). Second, we show that if a Meyer set is modified by addition and removal of points in such a way that its density is not altered too much (the allowable amount being given explicitly as a proportion of the original density), then the newly obtained set still has a relatively dense set of Bragg peaks.
DOI : 10.4153/CJM-2012-032-1
Mots-clés : 52C23, diffraction, Meyer set, Bragg peaks 
Strungaru, Nicolae. On the Bragg Diffraction Spectra of a Meyer Set. Canadian journal of mathematics, Tome 65 (2013) no. 3, pp. 675-701. doi: 10.4153/CJM-2012-032-1
@article{10_4153_CJM_2012_032_1,
     author = {Strungaru, Nicolae},
     title = {On the {Bragg} {Diffraction} {Spectra} of a {Meyer} {Set}},
     journal = {Canadian journal of mathematics},
     pages = {675--701},
     year = {2013},
     volume = {65},
     number = {3},
     doi = {10.4153/CJM-2012-032-1},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-2012-032-1/}
}
TY  - JOUR
AU  - Strungaru, Nicolae
TI  - On the Bragg Diffraction Spectra of a Meyer Set
JO  - Canadian journal of mathematics
PY  - 2013
SP  - 675
EP  - 701
VL  - 65
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-2012-032-1/
DO  - 10.4153/CJM-2012-032-1
ID  - 10_4153_CJM_2012_032_1
ER  - 
%0 Journal Article
%A Strungaru, Nicolae
%T On the Bragg Diffraction Spectra of a Meyer Set
%J Canadian journal of mathematics
%D 2013
%P 675-701
%V 65
%N 3
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-2012-032-1/
%R 10.4153/CJM-2012-032-1
%F 10_4153_CJM_2012_032_1

Cité par Sources :