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Mat. Sb., 2005, Volume 196, Number 12, Pages 99–122 (Mi msb1444)  

This article is cited in 14 scientific papers (total in 14 papers)

Strong asymptotics of the Hermite–Padé approximants for a system of Stieltjes functions with Laguerre weight

V. G. Lysov

M. V. Keldysh Institute for Applied Mathematics, Russian Academy of Sciences

Abstract: The Hermite–Padé approximants with common denominator are considered for a pair of Stieltjes functions with weights $x^\alpha e^{-\beta_1x}$ and $x^\alpha e^{-\beta_2x}$, where $\alpha>-1$, $\beta_2>\beta_1>0$. On the basis of the method of the Riemann–Hilbert matrix problem the strong asymptotics of these approximants are found in the case $\beta_2/\beta_1<3+2\sqrt2$. The limiting distribution of the zeros of the denominators of the Hermite–Padé approximants is shown to be equal to the equilibrium measure of a certain Nikishin system.


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English version:
Sbornik: Mathematics, 2005, 196:12, 1815–1840

Bibliographic databases:

UDC: 517.53
MSC: 41A21, 42C05
Received: 28.03.2005 and 14.10.2005

Citation: V. G. Lysov, “Strong asymptotics of the Hermite–Padé approximants for a system of Stieltjes functions with Laguerre weight”, Mat. Sb., 196:12 (2005), 99–122; Sb. Math., 196:12 (2005), 1815–1840

Citation in format AMSBIB
\by V.~G.~Lysov
\paper Strong asymptotics of the Hermite--Pad\'e approximants for a system of Stieltjes functions with Laguerre weight
\jour Mat. Sb.
\yr 2005
\vol 196
\issue 12
\pages 99--122
\jour Sb. Math.
\yr 2005
\vol 196
\issue 12
\pages 1815--1840

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    This publication is cited in the following articles:
    1. Aptekarev A.I., Kuijlaars A.B.J., Van Assche W., “Asymptotics of Hermite-Padé rational approximants for two analytic functions with separated pairs of branch points (case of genus 0)”, Int. Math. Res. Pap. IMRP, 2008, rpm007, 128 pp.  mathscinet  zmath  isi
    2. Balogh F., Bertola M., “Regularity of a vector potential problem and its spectral curve”, J. Approx. Theory, 161:1 (2009), 353–370  crossref  mathscinet  zmath  isi
    3. V. N. Sorokin, “Generalized Pollaczek polynomials”, Sb. Math., 200:4 (2009), 577–595  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    4. A. I. Aptekarev, 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  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    5. D. N. Tulyakov, “Plancherel-Rotach type asymptotics for solutions of linear recurrence relations with rational coefficients”, Sb. Math., 201:9 (2010), 1355–1402  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    6. A. I. Aptekarev, V. G. Lysov, D. N. Tulyakov, “Random matrices with external source and the asymptotic behaviour of multiple orthogonal polynomials”, Sb. Math., 202:2 (2011), 155–206  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    7. A. I. Aptekarev, A. Kuijlaars, “Hermite–Padé approximations and multiple orthogonal polynomial ensembles”, Russian Math. Surveys, 66:6 (2011), 1133–1199  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    8. A. I. Aptekarev, “Integriruemye poludiskretizatsii giperbolicheskikh uravnenii – “skhemnaya” dispersiya i mnogomernaya perspektiva”, Preprinty IPM im. M. V. Keldysha, 2012, 020, 28 pp.  mathnet
    9. Aptekarev A. Arvesu J., “Asymptotics for Multiple Meixner Polynomials”, J. Math. Anal. Appl., 411:2 (2014), 485–505  crossref  mathscinet  zmath  isi  elib
    10. V. N. Sorokin, “Ob asimptoticheskikh rezhimakh sovmestnykh mnogochlenov Meiksnera”, Preprinty IPM im. M. V. Keldysha, 2016, 046, 32 pp.  mathnet  crossref
    11. Aptekarev A.I., “The Mhaskar–Saff Variational Principle and Location of the Shocks of Certain Hyperbolic Equations”, Modern Trends in Constructive Function Theory, Contemporary Mathematics, 661, ed. Hardin D. Lubinsky D. Simanek B., Amer Mathematical Soc, 2016, 167–186  crossref  mathscinet  zmath  isi
    12. 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
    13. V. G. Lysov, “Asymptotics of Jacobi–Piñeiro Polynomials and Functions of the Second Kind”, Math. Notes, 103:3 (2018), 495–498  mathnet  crossref  crossref  isi  elib
    14. G. López Lagomasino, W. Van Assche, “Riemann-Hilbert analysis for a Nikishin system”, Sb. Math., 209:7 (2018), 1019–1050  mathnet  crossref  crossref  adsnasa  isi  elib
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