Sufficient conditions for the spectrality of self-affine measures with prime determinant
Volume 220 / 2014
Studia Mathematica 220 (2014), 73-86
MSC: Primary 28A80; Secondary 42C05, 46C05.
DOI: 10.4064/sm220-1-4
Abstract
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.
