We study spectral properties of the self-affine measure $\mu_{ M,\mathcal { D}}$ generated by an expanding integer matrix $M\in M_n(\mathbb{ Z})$ and a consecutive collinear digit set $\mathcal { D}=\{ 0,1,\dots,q-1\}v$ where $v\in \mathbb{ Z}^n\setminus\{ 0\}$ and $q\ge 2$ is an integer. Some sufficient conditions for $\mu_{ M,\mathcal { D}}$ to be a spectral measure or to have infinitely many orthogonal exponentials are given. Moreover, for some special cases, we can obtain a necessary and sufficient condition on the spectrality of $\mu_{ M,\mathcal { D}}$. Our study generalizes the one dimensional results proved by Dai, { \it et al.} (\cite{ Dai-He-Lai_2013, Dai-He-Lau_2014}).
Categories: math.CA math.FA