Spectral property of self-affine measures on Rn

We study spectral properties of the self-affine measure μM,D generated by an expanding integer matrix M∈Mn(Z) and a consecutive collinear digit set D={0,1,…,q−1}v where v∈Zn∖{0} and q≥2 is an integer. Some sufficient conditions for μM,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 μM,D. Our study generalizes the one dimensional results proved by Dai, et al. [4,5].