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Izv. RAN. Ser. Mat., 2001, Volume 65, Issue 4, Pages 35–48 (Mi izv346)  

This article is cited in 8 scientific papers (total in 8 papers)

On the Van Vleck theorem for regular $C$-fractions with limit-periodic coefficients

V. I. Buslaev

Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: In this paper we investigate the convergence set of a regular $C$-fraction with limit-periodic coefficients. This investigation is based on a general assertion concerning the convergence of composites of linear-fractional transformations whose coefficients are limit-periodic functions depending holomorphically on a parameter. We show that the singularity set of such a $C$-fraction possesses an extremal property stated in terms of the transfinite diameter (capacity) of sets.

DOI: https://doi.org/10.4213/im346

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English version:
Izvestiya: Mathematics, 2001, 65:4, 673–686

Bibliographic databases:

MSC: 30B70, 40A15
Received: 07.12.2000

Citation: V. I. Buslaev, “On the Van Vleck theorem for regular $C$-fractions with limit-periodic coefficients”, Izv. RAN. Ser. Mat., 65:4 (2001), 35–48; Izv. Math., 65:4 (2001), 673–686

Citation in format AMSBIB
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\by V.~I.~Buslaev
\paper On the Van Vleck theorem for regular $C$-fractions with limit-periodic coefficients
\jour Izv. RAN. Ser. Mat.
\yr 2001
\vol 65
\issue 4
\pages 35--48
\mathnet{http://mi.mathnet.ru/izv346}
\crossref{https://doi.org/10.4213/im346}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1857709}
\zmath{https://zbmath.org/?q=an:1023.30009}
\transl
\jour Izv. Math.
\yr 2001
\vol 65
\issue 4
\pages 673--686
\crossref{https://doi.org/10.1070/IM2001v065n04ABEH000346}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33746844963}


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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 Convergence of Continued T-Fractions”, Proc. Steklov Inst. Math., 235 (2001), 29–43  mathnet  mathscinet  zmath
    2. V. I. Buslaev, “On the Baker–Gammel–Wills conjecture in the theory of Padé approximants”, Sb. Math., 193:6 (2002), 811–823  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    3. V. I. Buslaev, “Convergence of the Rogers–Ramanujan continued fraction”, Sb. Math., 194:6 (2003), 833–856  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    4. D. Barrios Rolanía, G. López Lagomasino, “Asymptotic behavior of solutions of general three term recurrence relations”, Adv Comput Math, 26:1-3 (2007), 9  crossref  mathscinet  zmath  isi  scopus
    5. A. I. Aptekarev, V. I. Buslaev, A. Martínez-Finkelshtein, S. P. Suetin, “Padé approximants, continued fractions, and orthogonal polynomials”, Russian Math. Surveys, 66:6 (2011), 1049–1131  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    6. Buslaev V.I., “An Estimate of the Capacity of Singular Sets of Functions That Are Defined by Continued Fractions”, Anal. Math., 39:1 (2013), 1–27  crossref  mathscinet  zmath  isi  elib  scopus
    7. V. I. Buslaev, “On the Van Vleck Theorem for Limit-Periodic Continued Fractions of General Form”, Proc. Steklov Inst. Math., 298 (2017), 68–93  mathnet  crossref  crossref  mathscinet  isi  elib
    8. V. I. Buslaev, “Continued fractions with limit periodic coefficients”, Sb. Math., 209:2 (2018), 187–205  mathnet  crossref  crossref  adsnasa  isi  elib
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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