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Mat. Zametki, 2016, Volume 100, Issue 6, Pages 790–799 (Mi mz11279)  

This article is cited in 7 scientific papers (total in 7 papers)

The Capacity of the Rational Preimage of a Compact Set

V. I. Buslaev

Steklov Mathematical Institute of Russian Academy of Sciences, Moscow

Abstract: It is shown that a well-known expression for the capacity of the preimage of a compact set under a polynomial map remains valid in the case of a rational map, provided that the standard capacity of the preimage is replaced by its capacity in the external field determined by the poles in $\mathbb C$ of the rational function determining the map.

Keywords: capacity, transfinite diameter, rational map, symmetric compact set.

Funding Agency Grant Number
Russian Foundation for Basic Research 15-01-07531
Ministry of Education and Science of the Russian Federation НШ-9110.2016.1
Russian Academy of Sciences - Federal Agency for Scientific Organizations
This work was supported in part by the program “Modern Problems of Theoretical Mathematics” of Branch of Mathematics, Russian Academy of Sciences, by the Russian Foundation for Basic Research under grant 15-01-07531, and by the program “Leading Scientific Schools” under grant NSh-9110.2016.1.


DOI: https://doi.org/10.4213/mzm11279

Full text: PDF file (493 kB)
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English version:
Mathematical Notes, 2016, 100:6, 781–790

Bibliographic databases:

UDC: 517.53
Received: 01.06.2016

Citation: V. I. Buslaev, “The Capacity of the Rational Preimage of a Compact Set”, Mat. Zametki, 100:6 (2016), 790–799; Math. Notes, 100:6 (2016), 781–790

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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  mathnet  crossref  crossref  mathscinet  isi  elib
    2. V. I. Buslaev, “Continued fractions with limit periodic coefficients”, Sb. Math., 209:2 (2018), 187–205  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    3. 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
    4. M. Ya. Mazalov, “On Bianalytic Capacities”, Math. Notes, 103:4 (2018), 672–677  mathnet  crossref  crossref  isi  elib
    5. V. I. Buslaev, “Convergence of a Limit Periodic Schur Continued Fraction”, Math. Notes, 107:5 (2020), 701–712  mathnet  crossref  crossref  isi  elib
    6. V. I. Buslaev, “Schur's Criterion for Formal Newton Series”, Math. Notes, 108:6 (2020), 884–888  mathnet  crossref  crossref
    7. V. I. Buslaev, “Neobkhodimye i dostatochnye usloviya prodolzhimosti funktsii do funktsii Shura”, Matem. sb., 211:12 (2020), 3–48  mathnet  crossref
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