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Orthogonal exponential functions of self-similar measures with consecutive digits in [formula omitted].

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Title: Orthogonal exponential functions of self-similar measures with consecutive digits in [formula omitted].
Authors: Wang, Zhi-Yong1 wzyzzql@163.com, Wang, Zhi-Min1 zmwanghu@163.com, Dong, Xin-Han1 xhdonghnsd@163.com, Zhang, Peng-Fei2 pfzhang@math.cuhk.edu.hk
Source: Journal of Mathematical Analysis & Applications. Nov2018, Vol. 467 Issue 2, p1148-1152. 5p.
Subjects: Consecutive interpreting, Orthogonal functions, Exponential functions, Fourier transforms, Mathematical constants
Abstract: Suppose that 0 < | ρ | < 1 and m ≥ 2 is an integer. Let μ ρ , m be the self-similar measure defined by μ ρ , m ( ⋅ ) = 1 m ∑ j = 0 m − 1 μ ρ , m ( ρ − 1 ( ⋅ ) − j ) . In this paper, we prove that L 2 ( μ ρ , m ) contains an infinite orthonormal set of exponential functions if and only if ρ = ± ( q / p ) 1 / r for some p , q , r ∈ N + with gcd ( p , q ) = 1 and gcd ( p , m ) > 1 . [ABSTRACT FROM AUTHOR]
Copyright of Journal of Mathematical Analysis & Applications 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
An: 131186265
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PubType: Academic Journal
PubTypeId: academicJournal
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  Data: Orthogonal exponential functions of self-similar measures with consecutive digits in [formula omitted].
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  Data: &lt;searchLink fieldCode=&quot;AR&quot; term=&quot;%22Wang%2C+Zhi-Yong%22&quot;&gt;Wang, Zhi-Yong&lt;/searchLink&gt;&lt;relatesTo&gt;1&lt;/relatesTo&gt;&lt;i&gt; wzyzzql@163.com&lt;/i&gt;&lt;br /&gt;&lt;searchLink fieldCode=&quot;AR&quot; term=&quot;%22Wang%2C+Zhi-Min%22&quot;&gt;Wang, Zhi-Min&lt;/searchLink&gt;&lt;relatesTo&gt;1&lt;/relatesTo&gt;&lt;i&gt; zmwanghu@163.com&lt;/i&gt;&lt;br /&gt;&lt;searchLink fieldCode=&quot;AR&quot; term=&quot;%22Dong%2C+Xin-Han%22&quot;&gt;Dong, Xin-Han&lt;/searchLink&gt;&lt;relatesTo&gt;1&lt;/relatesTo&gt;&lt;i&gt; xhdonghnsd@163.com&lt;/i&gt;&lt;br /&gt;&lt;searchLink fieldCode=&quot;AR&quot; term=&quot;%22Zhang%2C+Peng-Fei%22&quot;&gt;Zhang, Peng-Fei&lt;/searchLink&gt;&lt;relatesTo&gt;2&lt;/relatesTo&gt;&lt;i&gt; pfzhang@math.cuhk.edu.hk&lt;/i&gt;
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  Data: Suppose that 0 &lt; | ρ | &lt; 1 and m ≥ 2 is an integer. Let μ ρ , m be the self-similar measure defined by μ ρ , m ( ⋅ ) = 1 m ∑ j = 0 m − 1 μ ρ , m ( ρ − 1 ( ⋅ ) − j ) . In this paper, we prove that L 2 ( μ ρ , m ) contains an infinite orthonormal set of exponential functions if and only if ρ = &#177; ( q / p ) 1 / r for some p , q , r ∈ N + with gcd ( p , q ) = 1 and gcd ( p , m ) &gt; 1 . [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
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  Data: &lt;i&gt;Copyright of Journal of Mathematical Analysis &amp; Applications 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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RecordInfo BibRecord:
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      – Type: doi
        Value: 10.1016/j.jmaa.2018.07.062
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      – Code: eng
        Text: English
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      Pagination:
        PageCount: 5
        StartPage: 1148
    Subjects:
      – SubjectFull: Consecutive interpreting
        Type: general
      – SubjectFull: Orthogonal functions
        Type: general
      – SubjectFull: Exponential functions
        Type: general
      – SubjectFull: Fourier transforms
        Type: general
      – SubjectFull: Mathematical constants
        Type: general
    Titles:
      – TitleFull: Orthogonal exponential functions of self-similar measures with consecutive digits in [formula omitted].
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            NameFull: Wang, Zhi-Yong
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            NameFull: Wang, Zhi-Min
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            NameFull: Dong, Xin-Han
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              Text: Nov2018
              Type: published
              Y: 2018
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            – TitleFull: Journal of Mathematical Analysis & Applications
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