Geodesic
Sufficient conditions for the spectrality of self-affine measures with prime determinant
Jian-Lin Li1
1 College of Mathematics and Information Science Shaanxi Normal University Xi'an 710119, P.R. China
Studia Mathematica, Tome 220 (2014) no. 1, pp. 73-86 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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Let $\mu _{M,D}$ be a self-affine measure associated with an expanding matrix $M$ and a finite digit set $D$. We study the spectrality of $\mu _{M,D}$ when $|{\rm det}(M)|=|D|=p$ is a prime. We obtain several new sufficient conditions on $M$ and $D$ for $\mu _{M,D}$ 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.
DOI : 10.4064/sm220-1-4
Keywords: self affine measure associated expanding matrix finite digit set nbsp study spectrality det prime obtain several sufficient conditions spectral measure lattice spectrum application present properties digit sets integral self affine tiles which connected conjecture lagarias wang

Jian-Lin Li 1

1 College of Mathematics and Information Science Shaanxi Normal University Xi'an 710119, P.R. China 
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Jian-Lin Li. Sufficient conditions for the spectrality of self-affine measures with prime determinant. Studia Mathematica, Tome 220 (2014) no. 1, pp. 73-86. doi: 10.4064/sm220-1-4

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