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Mat. Sb., 2005, Volume 196, Number 8, Pages 3–20 (Mi msb1404)  

This article is cited in 34 scientific papers (total in 35 papers)

Ratio asymptotics of Hermite–Padé polynomials for Nikishin systems

A. I. Aptekareva, G. López Lagomasinob, I. Alvarez Rochac

a M. V. Keldysh Institute for Applied Mathematics, Russian Academy of Sciences
b Carlos III University of Madrid
c Polytechnic University of Madrid

Abstract: The existence of ratio asymptotics is proved for a sequence of multiple orthogonal polynomials with orthogonality relations distributed among a system of $m$ finite Borel measures with support on a bounded interval of the real line which form a so-called Nikishin system. For $m=1$ this result reduces to Rakhmanov's celebrated theorem on the ratio asymptotics for orthogonal polynomials on the real line.

DOI: https://doi.org/10.4213/sm1404

Full text: PDF file (344 kB)
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English version:
Sbornik: Mathematics, 2005, 196:8, 1089–1107

Bibliographic databases:

UDC: 517.53
MSC: 42C05, 41A21
Received: 18.10.2004

Citation: A. I. Aptekarev, G. López Lagomasino, I. Alvarez Rocha, “Ratio asymptotics of Hermite–Padé polynomials for Nikishin systems”, Mat. Sb., 196:8 (2005), 3–20; Sb. Math., 196:8 (2005), 1089–1107

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Rolanía D.B., de la Calle Ysern B., López Lagomasino G., “Ratio and relative asymptotics of polynomials orthogonal with respect to varying Denisov-type measures”, J. Approx. Theory, 139:1-2 (2006), 223–256  crossref  mathscinet  zmath  isi
    2. Aptekarev A.I., Kalyagin V., López Lagomasino G., Rocha I.A., “On the limit behavior of recurrence coefficients for multiple orthogonal polynomials”, J. Approx. Theory, 139:1-2 (2006), 346–370  crossref  mathscinet  zmath  isi  elib
    3. López García A., López Lagomasino G., “Ratio asymptotic of Hermite-Pade orthogonal polynomials for Nikishin systems. II”, Adv. Math., 218:4 (2008), 1081–1106  crossref  mathscinet  zmath  isi
    4. López García A., López Lagomasino G., “Relative asymptotic of multiple orthogonal polynomials for Nikishin systems”, J. Approx. Theory, 158:2 (2009), 214–241  crossref  mathscinet  zmath  isi
    5. Fidalgo Prieto U., López García A., López Lagomasino G., Sorokin V.N., “Mixed type multiple orthogonal polynomials for two Nikishin systems”, Constr. Approx., 32:2 (2010), 255–306  crossref  mathscinet  zmath  isi  elib
    6. López Lagomasino G., Pestana D., Rodríguez J.M., Yakubovich D, “Computation of conformal representations of compact Riemann surfaces”, Math. Comp., 79:269 (2010), 365–381  crossref  mathscinet  zmath  adsnasa  isi  elib
    7. López Lagomasino G., Rocha I.A., “A canonical family of multiple orthogonal polynomials for Nikishin systems”, J. Math. Anal. Appl., 372:2 (2010), 390–401  crossref  mathscinet  zmath  isi  elib
    8. Bertola M., Gekhtman M., Szmigielski J., “Cauchy biorthogonal polynomials”, J. Approx. Theory, 162:4 (2010), 832–867  crossref  mathscinet  zmath  isi  elib
    9. de la Calle Ysern B., “A walk through approximation theory”, Recent trends in orthogonal polynomials and approximation theory, Contemp. Math., 507, Amer. Math. Soc., Providence, RI, 2010, 25–86  crossref  mathscinet  zmath  isi
    10. López García A., “Asymptotics of multiple orthogonal polynomials for a system of two measures supported on a starlike set”, J. Approx. Theory, 163:9 (2011), 1146–1184  crossref  mathscinet  zmath  isi
    11. Fidalgo Prieto U., López Lagomasino G., “Nikishin systems are perfect”, Constr. Approx., 34:3 (2011), 297–356  crossref  mathscinet  zmath  isi
    12. Steven Delvaux, Holger Dette, “Zeros and ratio asymptotics for matrix orthogonal polynomials”, JAMA, 118:2 (2012), 657  crossref  mathscinet  zmath  isi
    13. Haneczok M., Van Assche W., “Interlacing Properties of Zeros of Multiple Orthogonal Polynomials”, J. Math. Anal. Appl., 389:1 (2012), 429–438  crossref  mathscinet  zmath  isi  elib
    14. S. Delvaux, A. López, G. López Lagomasino, “A family of Nikishin systems with periodic recurrence coefficients”, Sb. Math., 204:1 (2013), 43–74  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    15. A. I. Aptekarev, D. N. Tulyakov, “The leading term of the Plancherel-Rotach asymptotic formula for solutions of recurrence relations”, Sb. Math., 205:12 (2014), 1696–1719  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    16. M. A. Lapik, “Formula Buyarova–Rakhmanova dlya vneshnego polya v vektornoi zadache ravnovesiya logarifmicheskogo potentsiala”, Preprinty IPM im. M. V. Keldysha, 2014, 082, 15 pp.  mathnet
    17. Branquinho A. Fidalgo Prieto U. Foulquie Moreno A., “An Extension of Markov's Theorem”, Proc. Amer. Math. Soc., 142:10 (2014), 3491–3503  crossref  mathscinet  zmath  isi
    18. G. López Lagomasino, S. Medina Peralta, U. Fidalgo Prieto, “Hermite-Padé approximation for certain systems of meromorphic functions”, Sb. Math., 206:2 (2015), 225–241  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    19. M. A. Lapik, “Families of vector measures which are equilibrium measures in an external field”, Sb. Math., 206:2 (2015), 211–224  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    20. V. M. Buchstaber, V. N. Dubinin, V. A. Kaliaguine, B. S. Kashin, V. N. Sorokin, S. P. Suetin, D. N. Tulyakov, B. N. Chetverushkin, E. M. Chirka, A. A. Shkalikov, “Alexander Ivanovich Aptekarev (on his 60th birthday)”, Russian Math. Surveys, 70:5 (2015), 965–973  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    21. Van Assche W., “Ratio Asymptotics for Multiple Orthogonal Polynomials”, Modern Trends in Constructive Function Theory, Contemporary Mathematics, 661, eds. Hardin D., Lubinsky D., Simanek B., Amer Mathematical Soc, 2016, 73–85  crossref  mathscinet  zmath  isi
    22. Martinez-Finkelshtein A. Rakhmanov E.A., “Do Orthogonal Polynomials Dream of Symmetric Curves?”, Found. Comput. Math., 16:6 (2016), 1697–1736  crossref  mathscinet  zmath  isi  scopus
    23. Fidalgo U., “Convergent interpolatory quadrature schemes”, Appl. Numer. Math., 111 (2017), 111–143  crossref  mathscinet  zmath  isi  scopus
    24. 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  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    25. A. I. Aptekarev, M. A. Lapik, Yu. N. Orlov, “Asymptotic behavior of the spectrum of combination scattering at Stokes phonons”, Theoret. and Math. Phys., 193:1 (2017), 1480–1497  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    26. 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
    27. A. I. Aptekarev, S. A. Denisov, M. L. Yattselev, “Samosopryazhennye matritsy Yakobi na grafakh i sovmestno ortogonalnye mnogochleny”, Preprinty IPM im. M. V. Keldysha, 2018, 003, 27 pp.  mathnet  crossref  elib
    28. Lopez-Garcia A., Lopez Lagomasino G., “Nikishin Systems on Star-Like Sets: Ratio Asymptotics of the Associated Multiple Orthogonal Polynomials”, J. Approx. Theory, 225 (2018), 1–40  crossref  mathscinet  zmath  isi
    29. V. G. Lysov, “Asymptotics of Jacobi–Piñeiro Polynomials and Functions of the Second Kind”, Math. Notes, 103:3 (2018), 495–498  mathnet  crossref  crossref  mathscinet  isi  elib
    30. D. Barrios Rolanía, J. S. Geronimo, G. López Lagomasino, “High-order recurrence relations, Hermite-Padé approximation and Nikishin systems”, Sb. Math., 209:3 (2018), 385–420  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    31. 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
    32. Lopez-Garcia A., Lopez Lagomasino G., “Nikishin Systems on Star-Like Sets: Ratio Asymptotics of the Associated Multiple Orthogonal Polynomials, II”, J. Approx. Theory, 250 (2020), UNSP 105320  crossref  mathscinet  isi
    33. Fidalgo U., Lopez Lagomasino G., Medina Peralta S., “Asymptotic of Cauchy Biorthogonal Polynomials”, Mediterr. J. Math., 17:1 (2020), 22  crossref  mathscinet  zmath  isi
    34. Aptekarev I A. Denisov S.A. Yattselev M.L., “Self-Adjoint Jacobi Matrices on Trees and Multiple Orthogonal Polynomials”, Trans. Am. Math. Soc., 373:2 (2020), 875–917  crossref  mathscinet  zmath  isi
    35. V. G. Lysov, “Mixed Type Hermite–Padé Approximants for a Nikishin System”, Proc. Steklov Inst. Math., 311 (2020), 199–213  mathnet  crossref  crossref  mathscinet  isi  elib
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