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Sufficient conditions for the spectrality of self-affine measures with prime determinant

Volume 220 / 2014

Jian-Lin Li Studia Mathematica 220 (2014), 73-86 MSC: Primary 28A80; Secondary 42C05, 46C05. DOI: 10.4064/sm220-1-4


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.


  • Jian-Lin LiCollege of Mathematics and Information Science
    Shaanxi Normal University
    Xi'an 710119, P.R. China

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