Abstract:
An example of a Markov function f=const+ˆσf=const+ˆσ such that the three functions ff, f2f2, and f3f3 constitute a Nikishin system is given. It is conjectured that there exists a Markov function ff such that, for each n∈N, the system of f,f2,…,fn is a Nikishin system.
\Bibitem{Sue18}
\by S.~P.~Suetin
\paper On an Example of the Nikishin System
\jour Mat. Zametki
\yr 2018
\vol 104
\issue 6
\pages 918--929
\mathnet{http://mi.mathnet.ru/mzm12181}
\crossref{https://doi.org/10.4213/mzm12181}
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\transl
\jour Math. Notes
\yr 2018
\vol 104
\issue 6
\pages 905--914
\crossref{https://doi.org/10.1134/S0001434618110342}
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https://doi.org/10.4213/mzm12181
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This publication is cited in the following 12 articles:
S. P. Suetin, “O skalyarnykh podkhodakh k izucheniyu predelnogo raspredeleniya nulei mnogochlenov Ermita–Pade dlya sistemy Nikishina”, UMN, 80:1(481) (2025), 85–152
N. R. Ikonomov, S. P. Suetin, “On some potential-theoretic problems related to the asymptotics of Hermite–Padé polynomials”, Sb. Math., 215:8 (2024), 1053–1064
S. P. Suetin, “Convergence of Hermite–Padé rational approximations”, Russian Math. Surveys, 78:5 (2023), 967–969
S. P. Suetin, “Asymptotic properties of Hermite–Padé polynomials and Katz points”, Russian Math. Surveys, 77:6 (2022), 1149–1151
E. A. Rakhmanov, S. P. Suetin, “Approksimatsii Chebysheva–Pade dlya mnogoznachnykh funktsii”, Tr. MMO, 83, no. 2, MTsNMO, M., 2022, 319–344
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
E. A. Rakhmanov, S. P. Suetin, “Chebyshev–Padé approximants for multivalued functions”, Trans. Moscow Math. Soc., –
N. R. Ikonomov, S. P. Suetin, “Structure of the Nuttall partition for some class of four-sheeted Riemann surfaces”, Trans. Moscow Math. Soc., 2022, –
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
S. P. Suetin, “Hermite–Padé polynomials and Shafer quadratic approximations for multivalued analytic functions”, Russian Math. Surveys, 75:4 (2020), 788–790
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
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), 970–979
Citation in format AMSBIB
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