Spectral properties of certain Moran measures with consecutive and collinear digit sets
AbstractLet the {2\times 2} expanding matrix {R_{k}} be an integer Jordan matrix, i.e., {R_{k}=\operatorname{diag}(r_{k},s_{k})} or {R_{k}=J(p_{k})}, and let {D_{k}=\{0,1,\ldots,q_{k}-1\}v} with {v=(1,1)^{T}} and {2\leq q_{k}\leq p_{k},r_{k},s_{k}} for each natural number k. We show that the sequence of Hadamard triples {\{(R_{k},D_{k},C_{k})\}} admits a spectrum of the associated Moran measure provided that {\liminf_{k\to\infty}2q_{k}\lVert R_{k}^{-1}\rVert<1}.
2020 ◽
Vol 2020
(48)
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pp. 17-24
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2015 ◽
Vol 60
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pp. 356-361
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2002 ◽
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pp. 16
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2003 ◽
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pp. 137-149
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2007 ◽
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pp. 20-26
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1980 ◽
Vol 45
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pp. 2247-2253
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1993 ◽
Vol 58
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pp. 2337-2348
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