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Sierpinski-type spectral self-similar measures.

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Title: Sierpinski-type spectral self-similar measures.
Authors: Deng, Qi-Rong1 qrdeng@fjnu.edu.cn, Lau, Ka-Sing2 kslau@math.cuhk.edu.hk
Source: Journal of Functional Analysis. Sep2015, Vol. 269 Issue 5, p1310-1326. 17p.
Subjects: Self-similar processes, Measure theory, Contractions (Topology), Bernoulli numbers, Mathematical convolutions, Mathematical analysis
Abstract: We consider the Sierpinski-type self-similar measure μ ρ on R 2 with contraction ratio 0 < | ρ | < 1 , we show that μ ρ is a spectral measure if and only if | ρ | = 1 / ( 3 p ) for some integer p > 0 . A similar characterization for Bernoulli convolution is due to Dai [2] , over which ρ = 1 / ( 2 p ) . [ABSTRACT FROM AUTHOR]
Copyright of Journal of Functional Analysis is the property of Academic Press Inc. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
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DbLabel: Engineering Source
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  Data: Sierpinski-type spectral self-similar measures.
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  Data: We consider the Sierpinski-type self-similar measure μ ρ on R 2 with contraction ratio 0 &lt; | ρ | &lt; 1 , we show that μ ρ is a spectral measure if and only if | ρ | = 1 / ( 3 p ) for some integer p &gt; 0 . A similar characterization for Bernoulli convolution is due to Dai [2] , over which ρ = 1 / ( 2 p ) . [ABSTRACT FROM AUTHOR]
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  Data: &lt;i&gt;Copyright of Journal of Functional Analysis is the property of Academic Press Inc. and its content may not be copied or emailed to multiple sites without the copyright holder&#39;s express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.&lt;/i&gt; (Copyright applies to all Abstracts.)
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        Value: 10.1016/j.jfa.2015.06.013
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      – Code: eng
        Text: English
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        PageCount: 17
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    Subjects:
      – SubjectFull: Self-similar processes
        Type: general
      – SubjectFull: Measure theory
        Type: general
      – SubjectFull: Contractions (Topology)
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      – SubjectFull: Bernoulli numbers
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      – SubjectFull: Mathematical convolutions
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      – TitleFull: Sierpinski-type spectral self-similar measures.
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            NameFull: Lau, Ka-Sing
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              M: 09
              Text: Sep2015
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