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On the spectra of a class of Moran measures.
- Source :
-
Forum Mathematicum . Mar2024, Vol. 36 Issue 2, p377-387. 11p. - Publication Year :
- 2024
-
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]
- Subjects :
- *FOURIER transforms
Subjects
Details
- Language :
- English
- ISSN :
- 09337741
- Volume :
- 36
- Issue :
- 2
- Database :
- Academic Search Index
- Journal :
- Forum Mathematicum
- Publication Type :
- Academic Journal
- Accession number :
- 175678880
- Full Text :
- https://doi.org/10.1515/forum-2023-0029