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Matematicheskie Zametki, 2020, Volume 107, Issue 5, Pages 643–656
DOI: https://doi.org/10.4213/mzm12729 (Mi mzm12729) 		 
This article is cited in 6 scientific papers (total in 6 papers)

Convergence of a Limit Periodic Schur Continued Fraction

V. I. Buslaev

Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
Full-text PDF (530 kB) Citations (6)
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DOI: https://doi.org/10.4213/mzm12729
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.
Received: 26.06.2019
Revised: 04.12.2019
English version:
Mathematical Notes, 2020, Volume 107, Issue 5, Pages 701–712
DOI: https://doi.org/10.1134/S0001434620050016
Bibliographic databases:
Document Type: Article
UDC: 517.53
Language: Russian
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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    • This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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