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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2020, Volume 309, Pages 174–197
DOI: https://doi.org/10.4213/tm4080 (Mi tm4080) 		 
This article is cited in 7 scientific papers (total in 7 papers)

Scalar Equilibrium Problem and the Limit Distribution of Zeros of Hermite–Padé Polynomials of Type II

N. R. Ikonomova, S. P. Suetinb

a Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, 8 Acad. Georgi Bonchev str., Sofia, 1113, Bulgaria
b Steklov Mathematical Institute of Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119991 Russia
Full-text PDF (359 kB) Citations (7)
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DOI: https://doi.org/10.4213/tm4080
Abstract: Using the scalar equilibrium problem posed on the two-sheeted Riemann surface, we prove the existence of a limit distribution of the zeros of Hermite–Padé polynomials of type II for a pair of functions forming a Nikishin system. We discuss the relation of the results obtained here to some results of H. Stahl (1988) and present results of numerical experiments. The results of the present paper and those obtained in earlier papers of the second author are shown to be in good accordance with both H. Stahl's results and results of numerical experiments.
Keywords: Nikishin system, Hermite–Padé polynomials, equilibrium problem, potential theory, Riemann surfaces.
Funding agency Grant number
Russian Foundation for Basic Research 18-01-00764
The research of the second author was supported in part by the Russian Foundation for Basic Research, project no. 18-01-00764.
Received: September 23, 2019
Revised: November 22, 2019
Accepted: February 19, 2020
English version:
Proceedings of the Steklov Institute of Mathematics, 2020, Volume 309, Pages 159–182
DOI: https://doi.org/10.1134/S0081543820030128
Bibliographic databases:
Document Type: Article
UDC: 517.53
Language: Russian
Citation: N. R. Ikonomov, S. P. Suetin, “Scalar Equilibrium Problem and the Limit Distribution of Zeros of Hermite–Padé Polynomials of Type II”, Modern problems of mathematical and theoretical physics, Collected papers. On the occasion of the 80th birthday of Academician Andrei Alekseevich Slavnov, Trudy Mat. Inst. Steklova, 309, Steklov Math. Inst. RAS, Moscow, 2020, 174–197; Proc. Steklov Inst. Math., 309 (2020), 159–182
Citation in format AMSBIB
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\paper Scalar Equilibrium Problem and the Limit Distribution of Zeros of Hermite--Pad\'e Polynomials of Type II
\inbook Modern problems of mathematical and theoretical physics
\bookinfo Collected papers. On the occasion of the 80th birthday of Academician Andrei Alekseevich Slavnov
\serial Trudy Mat. Inst. Steklova
\yr 2020
\vol 309
\pages 174--197
\publ Steklov Math. Inst. RAS
\publaddr Moscow
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  • https://doi.org/10.4213/tm4080
  • https://www.mathnet.ru/eng/tm/v309/p174
    • This publication is cited in the following 7 articles:
    1. S. P. Suetin, “O skalyarnykh podkhodakh k izucheniyu predelnogo raspredeleniya nulei mnogochlenov Ermita–Pade dlya sistemy Nikishina”, UMN, 80:1(481) (2025), 85–152  mathnet  crossref
    2. N. R. Ikonomov, S. P. Suetin, “Struktura nattollovskogo razbieniya dlya nekotorogo klassa chetyrekhlistnykh rimanovykh poverkhnostei”, Tr. MMO, 83, no. 1, MTsNMO, M., 2022, 37–61  mathnet
    3. E. A. Rakhmanov, S. P. Suetin, “Approksimatsii Chebysheva–Pade dlya mnogoznachnykh funktsii”, Tr. MMO, 83, no. 2, MTsNMO, M., 2022, 319–344  mathnet
    4. V. G. Lysov, “Mnogourovnevye interpolyatsii dlya obobschennoi sistemy Nikishina na grafe-dereve”, Tr. MMO, 83, no. 2, MTsNMO, M., 2022, 345–361  mathnet
    5. N. R. Ikonomov, S. P. Suetin, “Structure of the Nuttall partition for some class of four-sheeted Riemann surfaces”, Trans. Moscow Math. Soc., 2022, –  mathnet  mathnet  crossref
    6. E. A. Rakhmanov, S. P. Suetin, “Chebyshev–Padé approximants for multivalued functions”, Trans. Moscow Math. Soc., –  mathnet  mathnet  crossref
    7. V. G. Lysov, “Multilevel interpolations for the generalized Nikishin system on a tree graph”, Trans. Moscow Math. Soc., –  mathnet  mathnet  crossref
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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