Spectral properties of certain Moran measures with consecutive and collinear digit sets

Hai-Hua Wu 2 , Yu-Min Li 1  and Xin-Han Dong 3
  • 1 School of Mathematics, Hunan University, 410082, Changsha, P. R. China
  • 2 School of Mathematics and Statistics, Changsha University of Science and Technology, 410114; and School of Mathematics, Hunan University, Changsha, P. R. China
  • 3 School of Mathematics, Hunan University, 410082, Changsha, P. R. China
Hai-Hua Wu
  • School of Mathematics and Statistics, Changsha University of Science and Technology, 410114; and School of Mathematics, Hunan University, Changsha, 410082, P. R. China
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, Yu-Min Li and Xin-Han Dong

Abstract

Let the 2×2 expanding matrix Rk be an integer Jordan matrix, i.e., Rk=diag(rk,sk) or Rk=J(pk), and let Dk={0,1,,qk-1}v with v=(1,1)T and 2qkpk,rk,sk for each natural number k. We show that the sequence of Hadamard triples {(Rk,Dk,Ck)} admits a spectrum of the associated Moran measure provided that lim infk2qkRk-1<1.

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