Let mu = mu{Rn,Bn} = delta R-1 1 B1 * delta(R2R1)-1B2 * .. . be a Borel probability measure with a compact support, where Rn E M2(Z), BnC 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(mu). 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 p...
