Abstract
Letμ=μ{Rn,Bn}=δR1−1B1⁎δ(R2R1)−1B2⁎⋯ be a Borel probability measure with a compact support, where Rn∈M2(Z), Bn⊂Z2 and (Rn,Bn,Ln) forms a Hadamard triple for all n≥1. In this paper, we consider the existence of exponential orthogonal basis in L2(μ). We extend the concept of equi-positive family in [1] to higher dimensions, and provide a new idea to characterize the spectrality of such measures. In details, we study the spectrality and non-spectrality of Moran-Sierpinski type measures specifically under some necessary assumptions. The partial findings of several previous studies are extended by this study, such as Cantor-Moran measures (An-Fu-Lai [1], An-He-He [3]), Moran-Sierpinski type measures (Wang-Dong [47]) and Moran-Cantor-Dust type measures (Chen-Liu-Su-Wang [9]).
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