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Sbornik: Mathematics, 2018, Volume 209, Issue 2, Pages 187–205
DOI: https://doi.org/10.1070/SM8687 (Mi sm8687) 		 
This article is cited in 6 scientific papers (total in 6 papers)

Continued fractions with limit periodic coefficients

V. I. Buslaev

Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
English version PDF (525 kB) Citations (6)
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DOI: https://doi.org/10.1070/SM8687
Abstract: The boundary properties of functions represented by limit periodic continued fractions of a fairly general form are investigated. Such functions are shown to have no single-valued meromorphic extension to any neighbourhood of any non-isolated boundary point of the set of convergence of the continued fraction. The boundary of the set of meromorphy has the property of symmetry in an external field determined by the parameters of the continued fraction.
Bibliography: 26 titles.
Keywords: continued fractions, Hankel determinants, meromorphic extension, transfinite diameter.
Funding agency Grant number
Russian Science Foundation 14-50-00005
This work was supported by the Russian Science Foundation under grant no. 14-50-00005.
Received: 29.02.2016 and 27.06.2017
Russian version:
Matematicheskii Sbornik, 2018, Volume 209, Number 2, Pages 47–65
DOI: https://doi.org/10.4213/sm8687
Bibliographic databases:
Document Type: Article
UDC: 517.53
MSC: 30A14, 30B70
Language: English
Original paper language: Russian
Citation: V. I. Buslaev, “Continued fractions with limit periodic coefficients”, Mat. Sb., 209:2 (2018), 47–65; Sb. Math., 209:2 (2018), 187–205
Citation in format AMSBIB
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    • This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Russian version PDF:70
    English version PDF:20
    References:57
    First page:21
     
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