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Mat. Zametki, 2018, Volume 104, Issue 6, Pages 918–929 (Mi mz12181)  

This article is cited in 4 scientific papers (total in 4 papers)

On an Example of the Nikishin System

S. P. Suetin

Steklov Mathematical Institute of Russian Academy of Sciences, Moscow

Abstract: An example of a Markov function $f=\mathrm{const}+\widehat{\sigma}$ such that the three functions $f$, $f^2$, and $f^3$ constitute a Nikishin system is given. It is conjectured that there exists a Markov function $f$ such that, for each $n\in\mathbb N$, the system of $f,f^2,…,f^n$ is a Nikishin system.

Keywords: Hermite–Padé polynomials, Angelesco system, Nikishin system.

Funding Agency Grant Number
Russian Foundation for Basic Research 18-01-00764
This work was supported in part by the Russian Foundation for Basic Research under grant 18-01-00764.


DOI: https://doi.org/10.4213/mzm12181

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English version:
Mathematical Notes, 2018, 104:6, 905–914

Bibliographic databases:

UDC: 517.53
Received: 05.09.2018

Citation: S. P. Suetin, “On an Example of the Nikishin System”, Mat. Zametki, 104:6 (2018), 918–929; Math. Notes, 104:6 (2018), 905–914

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. S. P. Suetin, “Existence of a three-sheeted Nutall surface for a certain class of infinite-valued analytic functions”, Russian Math. Surveys, 74:2 (2019), 363–365  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    2. S. P. Suetin, “Equivalence of a Scalar and a Vector Equilibrium Problem for a Pair of Functions Forming a Nikishin System”, Math. Notes, 106:6 (2019), 971–980  mathnet  crossref  crossref  isi  elib
    3. N. R. Ikonomov, S. P. Suetin, “Scalar Equilibrium Problem and the Limit Distribution of Zeros of Hermite–Padé Polynomials of Type II”, Proc. Steklov Inst. Math., 309 (2020), 159–182  mathnet  crossref  crossref  isi
    4. S. P. Suetin, “Polinomy Ermita–Pade i kvadratichnye approksimatsii Shafera dlya mnogoznachnykh analiticheskikh funktsii”, UMN, 75:4(454) (2020), 213–214  mathnet  crossref
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