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Tr. Mat. Inst. Steklova, 2020, Volume 309, Pages 174–197 (Mi tm4080)  

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

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.

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.


DOI: https://doi.org/10.4213/tm4080

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English version:
Proceedings of the Steklov Institute of Mathematics, 2020, 309, 159–182

Bibliographic databases:

UDC: 517.53
Received: September 23, 2019
Revised: November 22, 2019
Accepted: February 19, 2020

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, Tr. 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 Tr. Mat. Inst. Steklova
\yr 2020
\vol 309
\pages 174--197
\publ Steklov Math. Inst. RAS
\publaddr Moscow
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\crossref{https://doi.org/10.4213/tm4080}
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  • Труды Математического института им. В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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