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Spectrality of Cantor–Moran measures with three-element digit sets.
- Source :
-
Forum Mathematicum . Mar2024, Vol. 36 Issue 2, p429-445. 17p. - Publication Year :
- 2024
-
Abstract
- Let 0 < ρ < 1 and let { a j , b j , n j } j = 1 ∞ be a sequence of positive integers with an upper bound. Associated with them, there exists a unique Borel probability measure μ ρ , { 0 , a j , b j } , { n j } generated by the following infinite convolution of discrete measures: μ ρ , { 0 , a j , b j } , { n j } = δ ρ n 1 { 0 , a 1 , b 1 } ∗ δ ρ n 1 + n 2 { 0 , a 2 , b 2 } ∗ δ ρ n 1 + n 2 + n 3 { 0 , a 3 , b 3 } ∗ ⋯ , where gcd (a j , b j) = 1 for all j ∈ ℕ . In this paper, we show that L 2 (μ ρ , { 0 , a j , b j } , { n j } ) admits an exponential orthonormal basis if and only if the following two conditions are satisfied: (i) { a j , b j } ≡ { ± 1 } (mod 3) for all j ≥ 1 ; (ii) there exists a natural number r such that ρ - r ∈ 3 ℕ and n j ∈ r ℕ for all j ≥ 2 . [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 09337741
- Volume :
- 36
- Issue :
- 2
- Database :
- Academic Search Index
- Journal :
- Forum Mathematicum
- Publication Type :
- Academic Journal
- Accession number :
- 175678884
- Full Text :
- https://doi.org/10.1515/forum-2023-0114