1. On the spectra of a class of Moran measures.
- Author
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Chen, Ming-Liang, Cao, Jian, Wang, Jia-Lin, and Wang, Ye
- Subjects
- *
FOURIER transforms - Abstract
Let { A n } n = 1 ∞ be a sequence of expanding matrices with A n ∈ M 2 (ℤ) , and let { D n } n = 1 ∞ be a sequence of three-element digit sets with { x ∈ (0 , 1) 2 : ∑ d ∈ D n e 2 π i 〈 d , x 〉 = 0 } = { ± 1 3 (1 , i) t } , i ∈ { 1 , 2 } . The associated Moran measure generated by the infinite convolution μ { A n } , { D n } = δ A 1 - 1 D 1 * δ A 1 - 1 A 2 - 1 D 2 * δ A 1 - 1 A 2 - 1 A 3 - 1 D 3 * ⋯. In this paper, we give some necessary and sufficient conditions for μ { A n } , { D n } to be a spectral measure under some suitable conditions on A n and D n . [ABSTRACT FROM AUTHOR]
- Published
- 2024
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