Abstract:
A new approach to the problem of the zero distribution of type I Hermite–Padé polynomials for a pair of functions f1,f2f1,f2 forming a Nikishin system is discussed. Unlike the traditional vector approach, we give an answer in terms of a scalar equilibrium problem with harmonic external field which is posed on a two-sheeted Riemann surface.
Keywords:
Hermite–Padé polynomials, non-Hermitian orthogonal polynomials, distribution of zeros.
Citation:
S. P. Suetin, “On a new approach to the problem of distribution of zeros of Hermite–Padé polynomials for a Nikishin system”, Complex analysis, mathematical physics, and applications, Collected papers, Trudy Mat. Inst. Steklova, 301, MAIK Nauka/Interperiodica, Moscow, 2018, 259–275; Proc. Steklov Inst. Math., 301 (2018), 245–261
\Bibitem{Sue18}
\by S.~P.~Suetin
\paper On a~new approach to the problem of distribution of zeros of Hermite--Pad\'e polynomials for a~Nikishin system
\inbook Complex analysis, mathematical physics, and applications
\bookinfo Collected papers
\serial Trudy Mat. Inst. Steklova
\yr 2018
\vol 301
\pages 259--275
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
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\jour Proc. Steklov Inst. Math.
\yr 2018
\vol 301
\pages 245--261
\crossref{https://doi.org/10.1134/S0081543818040193}
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Linking options:
https://www.mathnet.ru/eng/tm3908
https://doi.org/10.1134/S037196851802019X
https://www.mathnet.ru/eng/tm/v301/p259
This publication is cited in the following 14 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
A. V. Komlov, R. V. Palvelev, “Zeros of discriminants constructed from Hermite–Padé polynomials of an algebraic function and their relation to branch points”, Sb. Math., 215:12 (2024), 1633–1665
V. G. Lysov, “Mnogourovnevye interpolyatsii dlya obobschennoi sistemy Nikishina na grafe-dereve”, Tr. MMO, 83, no. 2, MTsNMO, M., 2022, 345–361
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
V. G. Lysov, “Multilevel interpolations for the generalized Nikishin system on a tree graph”, Trans. Moscow Math. Soc., –
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, –
S. P. Suetin, “Interpolation properties of Hermite–Padé polynomials”, Russian Math. Surveys, 76:3 (2021), 543–545
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
V. G. Lysov, “Mixed Type Hermite–Padé Approximants for a Nikishin System”, Proc. Steklov Inst. Math., 311 (2020), 199–213
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
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
S. P. Suetin, “On an Example of the Nikishin System”, Math. Notes, 104:6 (2018), 905–914
Citation in format AMSBIB
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