Let be a self-affine measure associated with an expanding matrix M and a finite digit set D. We study the spectrality of when |det(M)| = |D| = p is a prime. We obtain several new sufficient conditions on M and D for to be a spectral measure with lattice spectrum. As an application, we present some properties of the digit sets of integral self-affine tiles, which are connected with a conjecture of Lagarias and Wang.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm220-1-4,
author = {Jian-Lin Li},
title = {Sufficient conditions for the spectrality of self-affine measures with prime determinant},
journal = {Studia Mathematica},
volume = {223},
year = {2014},
pages = {73-86},
zbl = {06245255},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm220-1-4}
}
Jian-Lin Li. Sufficient conditions for the spectrality of self-affine measures with prime determinant. Studia Mathematica, Tome 223 (2014) pp. 73-86. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm220-1-4/