Abstract
Let R=diag(2q,2q) with q≥2 be an expanding positive integer matrix, and letD={(00),(10),(01),(−1−1)} be a four-element digit set. Chen and Yan [6] in 2021 proved that the self-similar measure μR,D is a spectral measure. In this paper, we give a description of the structure of spectra of μR,D. By extending the maximal mapping to plane, we characterize all the maximal orthogonal sets of exponential functions of μR,D and we indeed obtain some sufficient conditions for the maximal orthonormal set to be or not to be a basis for the space L2(μR,D).
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