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Mat. Sb., 2015, Volume 206, Number 12, Pages 55–69 (Mi msb8557)  

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

An analogue of Polya's theorem for piecewise holomorphic functions

V. I. Buslaev

Steklov Mathematical Institute of Russian Academy of Sciences, Moscow

Abstract: A well-known result due to Polya for a function given by its holomorphic germ at $z=\infty$ is extended to the case of a piecewise holomorphic function on an arbitrary compact set in $\overline{\mathbb C}$. This result is applied to the problem of the existence of compact sets that have the minimum transfinite diameter in the external field of the logarithmic potential of a negative unit charge among all compact sets such that a certain multivalued analytic function is single-valued and piecewise holomorphic on their complement.
Bibliography: 13 titles.

Keywords: rational approximations, continued fractions, Hankel determinants, Padé approximants.

Funding Agency Grant Number
Russian Science Foundation 14-50-00005
This work is supported by the Russian Science Foundation under grant no. 14-50-00005.


DOI: https://doi.org/10.4213/sm8557

Full text: PDF file (563 kB)
References: PDF file   HTML file

English version:
Sbornik: Mathematics, 2015, 206:12, 1707–1721

Bibliographic databases:

UDC: 517.53
MSC: 30C80, 31A15
Received: 16.06.2015 and 21.10.2015

Citation: V. I. Buslaev, “An analogue of Polya's theorem for piecewise holomorphic functions”, Mat. Sb., 206:12 (2015), 55–69; Sb. Math., 206:12 (2015), 1707–1721

Citation in format AMSBIB
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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, “An analog of Gonchar's theorem for the $m$-point version of Leighton's conjecture”, Proc. Steklov Inst. Math., 293 (2016), 127–139  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    2. V. I. Buslaev, “The Capacity of the Rational Preimage of a Compact Set”, Math. Notes, 100:6 (2016), 781–790  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    3. S. P. Suetin, “An Analog of Pólya's Theorem for Multivalued Analytic Functions with Finitely Many Branch Points”, Math. Notes, 101:5 (2017), 888–898  mathnet  crossref  crossref  mathscinet  isi  elib
    4. 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
    5. V. I. Buslaev, “Continued fractions with limit periodic coefficients”, Sb. Math., 209:2 (2018), 187–205  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    6. V. I. Buslaev, “On Singular points of Meromorphic Functions Determined by Continued Fractions”, Math. Notes, 103:4 (2018), 527–536  mathnet  crossref  crossref  mathscinet  isi  elib
    7. E. A. Rakhmanov, “Zero distribution for Angelesco Hermite–Padé polynomials”, Russian Math. Surveys, 73:3 (2018), 457–518  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    8. S. P. Suetin, “On a new approach to the problem of distribution of zeros of Hermite–Padé polynomials for a Nikishin system”, Proc. Steklov Inst. Math., 301 (2018), 245–261  mathnet  crossref  crossref  mathscinet  isi  elib  elib
  • Математический сборник Sbornik: Mathematics (from 1967)
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