Geodesic
On some potential-theoretic problems related to the asymptotics of Hermite–Padé polynomials
Sbornik. Mathematics, Tome 215 (2024) no. 8, pp. 1053-1064
Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Some mixed potential-theoretic equilibrium problems are treated. These problems are motivated by the asymptotic properties of rational approximants based on type II Hermite–Padé polynomials for Nikishin systems of functions. Bibliography: 26 titles.
Keywords: potential-theoretic problems, mixed potentials, Nikishin system, Riemann surface.
Mots-clés : Hermite–Padé polynomials 
@article{SM_2024_215_8_a2,
     author = {N. R. Ikonomov and S. P. Suetin},
     title = {On some potential-theoretic problems related to the asymptotics of {Hermite{\textendash}Pad\'e} polynomials},
     journal = {Sbornik. Mathematics},
     pages = {1053--1064},
     year = {2024},
     volume = {215},
     number = {8},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2024_215_8_a2/}
}
TY  - JOUR
AU  - N. R. Ikonomov
AU  - S. P. Suetin
TI  - On some potential-theoretic problems related to the asymptotics of Hermite–Padé polynomials
JO  - Sbornik. Mathematics
PY  - 2024
SP  - 1053
EP  - 1064
VL  - 215
IS  - 8
UR  - http://geodesic.mathdoc.fr/item/SM_2024_215_8_a2/
LA  - en
ID  - SM_2024_215_8_a2
ER  - 
%0 Journal Article
%A N. R. Ikonomov
%A S. P. Suetin
%T On some potential-theoretic problems related to the asymptotics of Hermite–Padé polynomials
%J Sbornik. Mathematics
%D 2024
%P 1053-1064
%V 215
%N 8
%U http://geodesic.mathdoc.fr/item/SM_2024_215_8_a2/
%G en
%F SM_2024_215_8_a2
N. R. Ikonomov; S. P. Suetin. On some potential-theoretic problems related to the asymptotics of Hermite–Padé polynomials. Sbornik. Mathematics, Tome 215 (2024) no. 8, pp. 1053-1064. http://geodesic.mathdoc.fr/item/SM_2024_215_8_a2/

[1] A. I. Aptekarev and V. G. Lysov, “Systems of Markov functions generated by graphs and the asymptotics of their Hermite–Padé approximants”, Sb. Math., 201:2 (2010), 183–234 | DOI | MR | Zbl

[2] A. I. Aptekarev, A. I. Bogolyubskii and M. L. Yattselev, “Convergence of ray sequences of Frobenius–Padé approximants”, Sb. Math., 208:3 (2017), 313–334 | DOI | MR | Zbl

[3] F. G. Avkhadiev, I. R. Kayumov and S. R. Nasyrov, “Extremal problems in geometric function theory”, Russian Math. Surveys, 78:2 (2023), 211–271 | DOI | MR | Zbl

[4] A. I. Aptekarev, S. Yu. Dobrokhotov, D. N. Tulyakov and A. V. Tsvetkova, “Plancherel–Rotach type asymptotic formulae for multiple orthogonal Hermite polynomials and recurrence relations”, Izv. Math., 86:1 (2022), 32–91 | DOI | MR | Zbl

[5] V. I. Buslaev and S. P. Suetin, “On equilibrium problems related to the distribution of zeros of the Hermite–Padé polynomials”, Proc. Steklov Inst. Math., 290:1 (2015), 256–263 | DOI | MR | Zbl

[6] E. O. Dobrolyubov, N. R. Ikonomov, L. A. Knizhnerman and S. P. Suetin, Rational Hermite–Padé approximants vs Padé approximants. Numerical results, arXiv: 2306.07063

[7] E. O. Dobrolyubov, I. V. Polyakov, D. V. Millionshchikov and S. V. Krasnoshchekov, “Vibrational resonance phenomena of the OCS isotopologues studied by resummation of high-order Rayleigh–Schrödinger perturbation theory”, J. Quant. Spectrosc. Radiat. Transf., 316 (2024), 108909, 13 pp. | DOI

[8] V. N. Dubinin, “Green energy of discrete signed measure on concentric circles”, Izv. Math., 87:2 (2023), 265–283 | DOI | MR | Zbl

[9] A. A. Gonchar and E. A. Rakhmanov, “On the convergence of simultaneous Padé approximants for systems of functions of Markov type”, Proc. Steklov Inst. Math., 157 (1983), 31–50 | MR | Zbl

[10] A. A. Gonchar and E. A. Rakhmanov, “Equilibrium measure and the distribution of zeros of extremal polynomials”, Math. USSR-Sb., 53:1 (1986), 119–130 | DOI | MR | Zbl

[11] A. A. Gonchar, E. A. Rakhmanov and S. P. Suetin, “On the convergence of Padé approximations of orthogonal expansions”, Proc. Steklov Inst. Math., 200 (1993), 149–159 | MR | Zbl

[12] A. A. Gonchar, E. A. Rakhmanov and S. P. Suetin, “Padé–Chebyshev approximants for multivalued analytic functions, variation of equilibrium energy, and the $S$-property of stationary compact sets”, Russian Math. Surveys, 66:6 (2011), 1015–1048 | DOI | MR | Zbl

[13] P. Henrici, “An algorithm for analytic continuation”, SIAM J. Numer. Anal., 3:1 (1966), 67–78 | DOI | MR | Zbl

[14] N. S. Landkof, Foundations of modern potential theory, Grundlehren Math. Wiss., 180, Springer-Verlag, New York–Heidelberg, 1972, x+424 pp. | MR | Zbl

[15] V. G. Lysov, “Mixed type Hermite–Padé approximants for a Nikishin system”, Proc. Steklov Inst. Math., 311 (2020), 199–213 | DOI | MR | Zbl

[16] E. M. Nikishin, “The asymptotic behavior of linear forms for joint Padé approximations”, Soviet Math. (Iz. VUZ), 30:2 (1986), 43–52 | MR | Zbl

[17] E. M. Nikishin and V. N. Sorokin, Rational approximations and orthogonality, Transl. Math. Monogr., 92, Amer. Math. Soc., Providence, RI, 1991, viii+221 pp. | DOI | MR | Zbl

[18] E. A. Rakhmanov and S. P. Suetin, “The distribution of the zeros of the Hermite–Padé polynomials for a pair of functions forming a Nikishin system”, Sb. Math., 204:9 (2013), 1347–1390 | DOI | MR | Zbl

[19] E. A. Rakhmanov and S. P. Suetin, “Tschebyshev–Padé approximations for multivalued functions”, Tr. Mosk. Mat. Obs., 83, no. 2, MCCME, Moscow, 2022, 319–344 ; English transl., arXiv: 2106.01047

[20] V. N. Sorokin, “A generalization of the discrete Rodrigues formula for Meixner polynomials”, Sb. Math., 213:11 (2022), 1559–1581 | DOI | MR | Zbl

[21] V. N. Sorokin, “On polynomials defined by the discrete Rodrigues formula”, Math. Notes, 113:3 (2023), 420–433 | DOI | MR | Zbl

[22] H. Stahl, “The convergence of Padé approximants to functions with branch points”, J. Approx. Theory, 91:2 (1997), 139–204 | DOI | MR | Zbl

[23] S. P. Suetin, “On an example of the Nikishin system”, Math. Notes, 104:6 (2018), 905–914 | DOI | MR | Zbl

[24] S. P. Suetin, “Asymptotic properties of Hermite–Padé polynomials and Katz points”, Russian Math. Surveys, 77:6 (2022), 1149–1151 | DOI | MR | Zbl

[25] S. P. Suetin, “Convergence of Hermite–Padé rational approximations”, Russian Math. Surveys, 78:5 (2023), 967–969 | DOI | MR | Zbl

[26] L. N. Trefethen, “Numerical analytic continuation”, Jpn. J. Ind. Appl. Math., 40:3 (2023), 1587–1636 | DOI | MR | Zbl