Spectrality of a class of Moran measures on Rn with consecutive digit sets

摘要

Let {R-k}(k=1)(infinity) be a sequence of expanding integer matrices in M-n(Z), and let {D-k}(K=1)(infinity )be a sequence of finite digit sets with integer vectors in Z(n). In this paper, we prove that under certain conditions in terms of (R-k, D-k) for k >= 1, the Moran measure @@@ mu({Rk},{Dk}) := delta(R1-1D1) * delta(R1-1R2-1D2) * ... @@@ is a spectral measure. For the converse, we get a necessity condition for the admissible pair (R, D).

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