V. G. Lysov, “Mixed Type Hermite–Padé Approximants for a Nikishin System”, Analysis and mathematical physics, Collected papers. On the occasion of the 70th birthday of Professor Armen Glebovich Sergeev, Trudy Mat. Inst. Steklova, 311, Steklov Math. Inst., Moscow, 2020, 213–227; Proc. Steklov Inst. Math., 311 (2020), 199

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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2020, Volume 311, Pages 213–227
DOI: https://doi.org/10.4213/tm4146 (Mi tm4146)

This article is cited in 16 scientific papers (total in 16 papers)

Mixed Type Hermite–Padé Approximants for a Nikishin System

V. G. Lysov

Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, Miusskaya pl. 4, Moscow, 125047 Russia

Full-text PDF (245 kB) Citations (16)

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DOI: https://doi.org/10.4213/tm4146

Abstract: We consider the problem of mixed type Hermite–Padé approximants and prove that the Nikishin system is perfect for this problem. Using the method of a vector equilibrium problem, we find weak asymptotics and prove the convergence of the approximants along any rays in the index table. We also present an equivalent statement in the form of a matrix Riemann–Hilbert problem.

Keywords: mixed type Hermite–Padé approximants, Nikishin system, perfect system, vector logarithmic-potential equilibrium problem, convergence of rational approximants, matrix Riemann–Hilbert problem.

Received: April 22, 2020
Revised: June 23, 2020
Accepted: July 21, 2020

English version:
Proceedings of the Steklov Institute of Mathematics, 2020, Volume 311, Pages 199–213
DOI: https://doi.org/10.1134/S0081543820060127

Bibliographic databases:

Document Type: Article

UDC: 517.53

Language: Russian

Citation: V. G. Lysov, “Mixed Type Hermite–Padé Approximants for a Nikishin System”, Analysis and mathematical physics, Collected papers. On the occasion of the 70th birthday of Professor Armen Glebovich Sergeev, Trudy Mat. Inst. Steklova, 311, Steklov Math. Inst., Moscow, 2020, 213–227; Proc. Steklov Inst. Math., 311 (2020), 199–213

Citation in format AMSBIB

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Linking options:

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https://doi.org/10.4213/tm4146

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This publication is cited in the following 16 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
L.G. González Ricardo, G. López Lagomasino, “Strong asymptotics of multi-level Hermite-Padé polynomials”, Journal of Mathematical Analysis and Applications, 531:1 (2024), 127801
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
A. Martínez-Finkelshtein, R. Orive, J. Sánchez-Lara, “Electrostatic partners and zeros of orthogonal and multiple orthogonal polynomials”, Constr. Approx., 58:2 (2023), 271
L.G. González Ricardo, G. López Lagomasino, S. Medina Peralta, “On the convergence of multi-level Hermite-Padé approximants”, Physica D: Nonlinear Phenomena, 440 (2022), 133487
L. G. González Ricardo, G. López Lagomasino, “Strong asymptotic of Cauchy biorthogonal polynomials and orthogonal polynomials with varying measure”, Constr. Approx., 56:3 (2022), 577
A. P. Starovoitov, N. V. Ryabchenko, “O determinantnykh predstavleniyakh mnogochlenov Ermita–Pade”, Tr. MMO, 83, no. 1, MTsNMO, M., 2022, 17–35
V. G. Lysov, “Mnogourovnevye interpolyatsii dlya obobschennoi sistemy Nikishina na grafe-dereve”, Tr. MMO, 83, no. 2, MTsNMO, M., 2022, 345–361
A. P. Starovoitov, N. V. Ryabchenko, “On determinant representations of Hermite–Padé polynomials”, Trans. Moscow Math. Soc., –
V. G. Lysov, “Multilevel interpolations for the generalized Nikishin system on a tree graph”, Trans. Moscow Math. Soc., –
S. P. Suetin, “Interpolation properties of Hermite–Padé polynomials”, Russian Math. Surveys, 76:3 (2021), 543–545
A. I. Aptekarev, V. G. Lysov, “Multilevel interpolation for Nikishin systems and boundedness of Jacobi matrices on binary trees”, Russian Math. Surveys, 76:4 (2021), 726–728
A. P. Starovoitov, N. V. Ryabchenko, “Analogs of Schmidt's Formula for Polyorthogonal Polynomials of the First Type”, Math. Notes, 110:3 (2021), 409–417
N. R. Ikonomov, S. P. Suetin, “A Viskovatov algorithm for Hermite-Padé polynomials”, Sb. Math., 212:9 (2021), 1279–1303
V. N. Sorokin, “Multipoint Padé Approximation of the Psi Function”, Math. Notes, 110:4 (2021), 571–577
A. V. Komlov, “The polynomial Hermite-Padé $m$ -system for meromorphic functions on a compact Riemann surface”, Sb. Math., 212:12 (2021), 1694–1729

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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