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Sbornik: Mathematics, 2017, Volume 208, Issue 3, Pages 313–334
DOI: https://doi.org/10.1070/SM8632
(Mi sm8632)
 

This article is cited in 13 scientific papers (total in 13 papers)

Convergence of ray sequences of Frobenius-Padé approximants

A. I. Aptekareva, A. I. Bogolyubskiib, M. Yattselevc

a Federal Research Centre Keldysh Institute of Applied Mathematics of Russian Academy of Sciences, Moscow
b Russian National Research Medical University named after N. I. Pirogov, Moscow
c Department of Mathematical Sciences, Indiana University – Purdue University Indianapolis, Indianapolis, IN, USA
References:
Abstract: Let ˆσˆσ be a Cauchy transform of a possibly complex-valued Borel measure σσ and {pn}{pn} a system of orthonormal polynomials with respect to a measure μμ, where supp(μ)supp(σ)=. An (m,n)th Frobenius-Padé approximant to ˆσ is a rational function P/Q, deg(P)m, deg(Q)n, such that the first m+n+1 Fourier coefficients of the remainder function QˆσP vanish when the form is developed into a series with respect to the polynomials pn. We investigate the convergence of the Frobenius-Padé approximants to ˆσ along ray sequences n/(n+m+1)c>0, n1m, when μ and σ are supported on intervals of the real line and their Radon-Nikodym derivatives with respect to the arcsine distribution of the corresponding interval are holomorphic functions.
Bibliography: 30 titles.
Keywords: Frobenius-Padé approximants, linear Padé-Chebyshev approximants, Padé approximants of orthogonal expansions, orthogonality, Markov-type functions, Riemann-Hilbert matrix problem.
Funding agency Grant number
Russian Science Foundation 14-21-00025
Russian Foundation for Basic Research 14-01-00604-a
17-01-00614-a
Simons Foundation #354538
A. I. Aptekarev's research was supported by the Russian Science Foundation (grant no. 14-21-00025). A. I. Bogolyubskii's research was supported by the Russian Foundation for Basic Research (grant nos. 14-01-00604_а and 17-01-00614_a). M. L. Yattselev's research was supported by the Simons Foundation (grant #354538).
Received: 09.11.2015 and 26.09.2016
Bibliographic databases:
Document Type: Article
UDC: 517.53
MSC: 41A20, 41A21
Language: English
Original paper language: Russian
Citation: A. I. Aptekarev, A. I. Bogolyubskii, M. Yattselev, “Convergence of ray sequences of Frobenius-Padé approximants”, Sb. Math., 208:3 (2017), 313–334
Citation in format AMSBIB
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\paper Convergence of ray sequences of Frobenius-Pad\'e approximants
\jour Sb. Math.
\yr 2017
\vol 208
\issue 3
\pages 313--334
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Linking options:
  • https://www.mathnet.ru/eng/sm8632
  • https://doi.org/10.1070/SM8632
  • https://www.mathnet.ru/eng/sm/v208/i3/p4
  • This publication is cited in the following 13 articles:
    1. Methawee Wajasat, Nattapong Bosuwan, “Rate of pole detection using Padé approximants to polynomial expansions”, Demonstratio Mathematica, 58:1 (2025)  crossref
    2. 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  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    3. A. I. Aptekarev, S. A. Denisov, M. L. Yattselev, “Jacobi matrices on trees generated by Angelesco systems: asymptotics of coefficients and essential spectrum”, J. Spectr. Theory, 11:4 (2021), 1511–1597  crossref  mathscinet  isi
    4. 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  mathnet  crossref  crossref  mathscinet  isi  elib
    5. A. I. Bogolyubskii, V. G. Lysov, “Constructive solution of one vector equilibrium problem”, Dokl. Math., 101:2 (2020), 90–92  mathnet  crossref  crossref  zmath  elib
    6. 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  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    7. 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  mathnet  crossref  crossref  mathscinet  isi  elib
    8. S. P. Suetin, “Distribution of the zeros of Hermite–Padé polynomials for a complex Nikishin system”, Russian Math. Surveys, 73:2 (2018), 363–365  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    9. G. López Lagomasino, W. Van Assche, “Riemann-Hilbert analysis for a Nikishin system”, Sb. Math., 209:7 (2018), 1019–1050  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    10. S. P. Suetin, “On a new approach to the problem of distribution of zeros of Hermite–Padé polynomials for a Nikishin system”, Proc. Steklov Inst. Math., 301 (2018), 245–261  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    11. A. P. Starovoitov, “Hermite–Padé approximants of the Mittag-Leffler functions”, Proc. Steklov Inst. Math., 301 (2018), 228–244  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    12. S. P. Suetin, “On an Example of the Nikishin System”, Math. Notes, 104:6 (2018), 905–914  mathnet  crossref  crossref  mathscinet  isi  elib
    13. V. G. Lysov, “Silnaya asimptotika approksimatsii Ermita–Pade dlya sistemy Nikishina s vesami Yakobi”, Preprinty IPM im. M. V. Keldysha, 2017, 085, 35 pp.  mathnet  crossref
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