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Tr. Mat. Inst. Steklova, 2015, Volume 290, Pages 272–279 (Mi tm3645)  

This article is cited in 22 scientific papers (total in 22 papers)

On equilibrium problems related to the distribution of zeros of the Hermite–Padé polynomials

V. I. Buslaev, S. P. Suetin

Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russia

Abstract: We study two potential-theory equilibrium problems that arise naturally in the theory of the limit distribution of zeros of the Hermite–Padé polynomials. We analyze the relationship between these problems and prove that the equilibrium measure for one of the problems is the balayage of the equilibrium measure for the other problem.

Funding Agency Grant Number
Russian Science Foundation 14-50-00005
This work is supported by the Russian Science Foundation under grant 14-50-00005.


DOI: https://doi.org/10.1134/S037196851503022X

Full text: PDF file (196 kB)
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English version:
Proceedings of the Steklov Institute of Mathematics, 2015, 290:1, 256–263

Bibliographic databases:

Document Type: Article
UDC: 517.53
Received: March 15, 2015

Citation: V. I. Buslaev, S. P. Suetin, “On equilibrium problems related to the distribution of zeros of the Hermite–Padé polynomials”, Modern problems of mathematics, mechanics, and mathematical physics, Collected papers, Tr. Mat. Inst. Steklova, 290, MAIK Nauka/Interperiodica, Moscow, 2015, 272–279; Proc. Steklov Inst. Math., 290:1 (2015), 256–263

Citation in format AMSBIB
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\bookinfo Collected papers
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\vol 290
\pages 272--279
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
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  • https://doi.org/10.1134/S037196851503022X
  • http://mi.mathnet.ru/eng/tm/v290/p272

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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. S. P. Suetin, “Distribution of the zeros of Padé polynomials and analytic continuation”, Russian Math. Surveys, 70:5 (2015), 901–951  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    2. A. V. Komlov, N. G. Kruzhilin, R. V. Palvelev, S. P. Suetin, “Convergence of Shafer quadratic approximants”, Russian Math. Surveys, 71:2 (2016), 373–375  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    3. 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
    4. A. Martinez-Finkelshtein, E. .A. Rakhmanov, S. P. Suetin, “Asymptotics of Type I Hermite-Padé Polynomials for Semiclassical Functions”, Modern Trends in Constructive Function Theory, Conference and School on Constructive Functions in honor of Ed Saff's 70th Birthday Location (Vanderbilt Univ, Nashville, TN, 2014), Contemporary Mathematics, 661, 2016, 199–228  crossref  mathscinet  zmath  isi
    5. E. A. Rakhmanov, “The Gonchar-Stahl $\rho^2$-theorem and associated directions in the theory of rational approximations of analytic functions”, Sb. Math., 207:9 (2016), 1236–1266  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    6. S. P. Suetin, “Zero distribution of Hermite–Padé polynomials and localization of branch points of multivalued analytic functions”, Russian Math. Surveys, 71:5 (2016), 976–978  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    7. 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
    8. S. P. Suetin, “On the distribution of the zeros of the Hermite–Padé polynomials for a quadruple of functions”, Russian Math. Surveys, 72:2 (2017), 375–377  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    9. 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
    10. A. V. Komlov, R. V. Palvelev, S. P. Suetin, E. M. Chirka, “Hermite–Padé approximants for meromorphic functions on a compact Riemann surface”, Russian Math. Surveys, 72:4 (2017), 671–706  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    11. 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
    12. V. G. Lysov, D. N. Tulyakov, “On a Vector Potential-Theory Equilibrium Problem with the Angelesco Matrix”, Proc. Steklov Inst. Math., 298 (2017), 170–200  mathnet  crossref  crossref  isi  elib
    13. A. P. Starovoitov, E. P. Kechko, “On Some Properties of Hermite–Padé Approximants to an Exponential System”, Proc. Steklov Inst. Math., 298 (2017), 317–333  mathnet  crossref  crossref  isi  elib
    14. V. I. Buslaev, “Continued fractions with limit periodic coefficients”, Sb. Math., 209:2 (2018), 187–205  mathnet  crossref  crossref  adsnasa  isi  elib
    15. V. I. Buslaev, “On Singular points of Meromorphic Functions Determined by Continued Fractions”, Math. Notes, 103:4 (2018), 527–536  mathnet  crossref  crossref  isi  elib
    16. M. V. Sidortsov, A. A. Drapeza, A. P. Starovoitov, “Skorost skhodimosti kvadratichnykh approksimatsii Ermita–Pade vyrozhdennykh gipergeometricheskikh funktsii”, PFMT, 2018, no. 1(34), 71–78  mathnet
    17. S. P. Suetin, “Distribution of the zeros of Hermite–Padé polynomials for a complex Nikishin system”, Russian Math. Surveys, 73:2 (2018), 363–365  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    18. E. A. Rakhmanov, “Zero distribution for Angelesco Hermite–Padé polynomials”, Russian Math. Surveys, 73:3 (2018), 457–518  mathnet  crossref  crossref  adsnasa  isi  elib
    19. 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  isi
    20. V. G. Lysov, D. N. Tulyakov, “On the supports of vector equilibrium measures in the Angelesco problem with nested intervals”, Proc. Steklov Inst. Math., 301 (2018), 180–196  mathnet  crossref  crossref  isi
    21. A. P. Starovoitov, “Hermite–Padé approximants of the Mittag-Leffler functions”, Proc. Steklov Inst. Math., 301 (2018), 228–244  mathnet  crossref  crossref  isi
    22. E. M. Chirka, “Potentials on a compact Riemann surface”, Proc. Steklov Inst. Math., 301 (2018), 272–303  mathnet  crossref  crossref  isi
  • Труды Математического института им. В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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