Spectrality of Moran-Type Bernoulli Convolutions

Let p n , d n ∈ Z be integers such that | p n | > | d n | > 0 and { d n } n ≥ 1 is bounded. It is proven that the Moran-type Bernoulli convolution μ : = δ p 1 - 1 { 0 , d 1 } ∗ δ p 1 - 1 p 2 - 1 { 0 , d 2 } ∗ ⋯ ∗ δ p 1 - 1 ⋯ p n - 1 { 0 , d n } ∗ ⋯ is a spectral measure if and only if the numb...

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Bibliographic Details
Published in:Bulletin of the Malaysian Mathematical Sciences Society 2023-07, Vol.46 (4), Article 136
Main Authors: Deng, Qi-Rong, Li, Ming-Tian
Format: Article
Language:English
Subjects:
Applications of Mathematics
Mathematics
Mathematics and Statistics
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Summary:Let p n , d n ∈ Z be integers such that | p n | > | d n | > 0 and { d n } n ≥ 1 is bounded. It is proven that the Moran-type Bernoulli convolution μ : = δ p 1 - 1 { 0 , d 1 } ∗ δ p 1 - 1 p 2 - 1 { 0 , d 2 } ∗ ⋯ ∗ δ p 1 - 1 ⋯ p n - 1 { 0 , d n } ∗ ⋯ is a spectral measure if and only if the numbers of factor 2 in the sequence { p 1 p 2 ⋯ p n 2 d n } n ≥ 1 are different from each other.
ISSN:0126-6705
2180-4206
DOI:10.1007/s40840-023-01532-z