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Mat. Zametki, 2020, Volume 107, Issue 5, Pages 643–656 (Mi mz12729)  

This article is cited in 3 scientific papers (total in 3 papers)

Convergence of a Limit Periodic Schur Continued Fraction

V. I. Buslaev

Steklov Mathematical Institute of Russian Academy of Sciences, Moscow

Abstract: In this paper, we show that if the parameters of a Schur continued fraction tend to zero, then the functions to which the even convergents converge inside the unit disk and the functions to which the odd convergents converge outside the unit disk cannot have a meromorphic continuation to each other through any arc of the unit circle. This result is obtained as a consequence of the convergence theorem for limit periodic Schur continued fractions.

Keywords: continued fractions, Hankel determinants, transfinite diameter, meromorphic continuation.

Funding Agency Grant Number
Russian Science Foundation 19-11-00316
This work was supported by the Russian Science Foundation under grant 19-11-00316.


DOI: https://doi.org/10.4213/mzm12729

Full text: PDF file (530 kB)
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English version:
Mathematical Notes, 2020, 107:5, 701–712

Bibliographic databases:

UDC: 517.53
Received: 26.06.2019
Revised: 04.12.2019

Citation: V. I. Buslaev, “Convergence of a Limit Periodic Schur Continued Fraction”, Mat. Zametki, 107:5 (2020), 643–656; Math. Notes, 107:5 (2020), 701–712

Citation in format AMSBIB
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\paper Convergence of a Limit Periodic Schur Continued Fraction
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\pages 643--656
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  • https://doi.org/10.4213/mzm12729
  • http://mi.mathnet.ru/eng/mz/v107/i5/p643

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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, “Schur's Criterion for Formal Newton Series”, Math. Notes, 108:6 (2020), 884–888  mathnet  crossref  crossref  mathscinet  isi  elib
    2. V. I. Buslaev, “Necessary and sufficient conditions for extending a function to a Schur function”, Sb. Math., 211:12 (2020), 1660–1703  mathnet  crossref  crossref  mathscinet  isi  elib
    3. 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  mathnet  crossref  crossref  isi  elib
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