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 Mat. Sb., 2018, Volume 209, Number 2, Pages 47–65 (Mi msb8687)

Continued fractions with limit periodic coefficients

V. I. Buslaev

Steklov Mathematical Institute of Russian Academy of Sciences, Moscow

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.

DOI: https://doi.org/10.4213/sm8687

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English version:
Sbornik: Mathematics, 2018, 209:2, 187–205

Bibliographic databases:

UDC: 517.53
MSC: 30A14, 30B70

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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• http://mi.mathnet.ru/eng/msb8687
• https://doi.org/10.4213/sm8687
• http://mi.mathnet.ru/eng/msb/v209/i2/p47

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. V. I. Buslaev, “On the Van Vleck Theorem for Limit-Periodic Continued Fractions of General Form”, Proc. Steklov Inst. Math., 298 (2017), 68–93
2. V. I. Buslaev, “On Singular points of Meromorphic Functions Determined by Continued Fractions”, Math. Notes, 103:4 (2018), 527–536
3. V. I. Buslaev, “Schur's criterion for formal power series”, Sb. Math., 210:11 (2019), 1563–1580
4. V. I. Buslaev, “Convergence of a Limit Periodic Schur Continued Fraction”, Math. Notes, 107:5 (2020), 701–712
5. V. I. Buslaev, “Necessary and sufficient conditions for extending a function to a Schur function”, Sb. Math., 211:12 (2020), 1660–1703
6. V. I. Buslaev, “On a lower bound for the rate of convergence of multipoint Padé approximants of piecewise analytic functions”, Izv. Math., 85:3 (2021), 351–366
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