Abstract:
The problem of the limiting distribution of the zeros and the asymptotic behaviour of the Hermite–Padé polynomials of the first kind is considered for a system of germs [1,f1,∞,…,fm,∞] of meromorphic functions fj, j=1,…,m, on an (m+1)-sheeted Riemann surface R. Nuttall's approach to the solution of this problem, based on a particular ‘Nuttall’ partition of R into sheets, is further developed.
Bibliography: 36 titles.
Keywords:
rational approximants, Hermite–Padé polynomials, distribution of zeros, convergence in capacity.
Citation:
A. V. Komlov, R. V. Palvelev, S. P. Suetin, E. M. Chirka, “Hermite–Padé approximants for meromorphic functions on a compact Riemann surface”, Russian Math. Surveys, 72:4 (2017), 671–706
This publication is cited in the following 30 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
S. P. Suetin, “Maximum principle and asymptotic properties of Hermite–Padé polynomials”, Russian Math. Surveys, 79:3 (2024), 547–549
Huck Stepanyants, Alan Beardon, Jeremy Paton, Dmitri Krioukov, “Computing distances on Riemann surfaces”, J. Phys. A: Math. Theor., 57:34 (2024), 345201
S. R. Nasyrov, “Nuttall decomposition of a three-sheeted torus”, Izv. Math., 88:5 (2024), 873–929
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
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, “Approksimatsii Chebysheva–Pade dlya mnogoznachnykh funktsii”, Tr. MMO, 83, no. 2, MTsNMO, M., 2022, 319–344
V. G. Lysov, “Mnogourovnevye interpolyatsii dlya obobschennoi sistemy Nikishina na grafe-dereve”, Tr. MMO, 83, no. 2, MTsNMO, M., 2022, 345–361
N. R. Ikonomov, S. P. Suetin, “Structure of the Nuttall partition for some class of four-sheeted Riemann surfaces”, Trans. Moscow Math. Soc., 2022, –
E. A. Rakhmanov, S. P. Suetin, “Chebyshev–Padé approximants for multivalued functions”, 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, “Two Examples Related to Properties of Discrete Measures”, Math. Notes, 110:4 (2021), 578–582
A. V. Komlov, “The polynomial Hermite-Padé $m$-system for meromorphic functions on a compact Riemann surface”, Sb. Math., 212:12 (2021), 1694–1729
Aleksandr Komlov, Trends in Mathematics, 12, Extended Abstracts Fall 2019, 2021, 113
A. I. Aptekarev, S. A. Denisov, M. L. Yattselev, “Self-adjoint Jacobi matrices on trees and multiple orthogonal polynomials”, Trans. Am. Math. Soc., 373:2 (2020), 875–917
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
V. G. Lysov, “Mixed Type Hermite–Padé Approximants for a Nikishin System”, Proc. Steklov Inst. Math., 311 (2020), 199–213
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
V. G. Lysov, “Asymptotics of Jacobi–Piñeiro Polynomials and Functions of the Second Kind”, Math. Notes, 103:3 (2018), 495–498
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