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Mat. Sb., 1992, Volume 183, Number 11, Pages 117–138 (Mi msb1092)  

This article is cited in 40 scientific papers (total in 40 papers)

Hermite–Padé approximation for Nikishin systems of analytic functions

Zh. Bustamante, G. López Lagomasino

Abstract: Nikishin type systems of analytic functions are considered. For such systems, convergence of the main diagonal of the associated Hermite-Padé approximants is proved, when interpolation is equally distributed between the functions. If interpolation is 'nearly' equally distributed, then convergence in capacity takes place. Multipoint Padé approximation plays a key role in the proof.

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English version:
Russian Academy of Sciences. Sbornik. Mathematics, 1994, 77:2, 367–384

Bibliographic databases:

UDC: 517.53
MSC: Primary 30E10; Secondary 41A21
Received: 15.10.1991

Citation: Zh. Bustamante, G. López Lagomasino, “Hermite–Padé approximation for Nikishin systems of analytic functions”, Mat. Sb., 183:11 (1992), 117–138; Russian Acad. Sci. Sb. Math., 77:2 (1994), 367–384

Citation in format AMSBIB
\by Zh.~Bustamante, G.~L\'opez Lagomasino
\paper Hermite--Pad\'e approximation for Nikishin systems of analytic functions
\jour Mat. Sb.
\yr 1992
\vol 183
\issue 11
\pages 117--138
\jour Russian Acad. Sci. Sb. Math.
\yr 1994
\vol 77
\issue 2
\pages 367--384

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    This publication is cited in the following articles:
    1. Bustamante J., Lagomasino G., “Rate of Convergence of Hermite-Pade Approximants to a Nikishin-Type System of Analytic-Functions”, J. Comput. Appl. Math., 49:1-3 (1993), 19–25  crossref  mathscinet  zmath  isi
    2. Debruin M., Driver K., Lubinsky D., “Convergence of Simultaneous Hermite-Pade Approximants to the N-Tuple of Q-Hypergeometric Series ((2)Phi(0)((a,Alpha(J)), (1,1) Z))(J=1)(N)”, J. Comput. Appl. Math., 49:1-3 (1993), 37–43  crossref  mathscinet  isi
    3. V. A. Kalyagin, “Hermite–Padé approximants and spectral analysis of nonsymmetric operators”, Russian Acad. Sci. Sb. Math., 82:1 (1995), 199–216  mathnet  crossref  mathscinet  zmath  isi
    4. Bustamante J., Lagomasino G., “Hermite-Pade Approximation to a Nikishin Type System of Meromorphic Functions”, J. Approx. Theory, 81:1 (1995), 1–12  crossref  mathscinet  zmath  isi
    5. Gonzalez J., “Asymptotics for Angelesco-Nikishin Systems”, J. Approx. Theory, 85:1 (1996), 43–68  crossref  mathscinet  zmath  isi
    6. A. A. Gonchar, E. A. Rakhmanov, V. N. Sorokin, “Hermite–Pade approximants for systems of Markov-type functions”, Sb. Math., 188:5 (1997), 671–696  mathnet  crossref  crossref  mathscinet  zmath  isi
    7. B de la Calle Ysern, G López Lagomasino, “Strong asymptotics of orthogonal polynomials with varying measures and Hermite-Padé approximants”, Journal of Computational and Applied Mathematics, 99:1-2 (1998), 91  crossref
    8. A.I. Aptekarev, “Multiple orthogonal polynomials”, Journal of Computational and Applied Mathematics, 99:1-2 (1998), 423  crossref
    9. Ysern B., Lagomasino G., “Strong Asymptotics of Orthogonal Polynomials with Varying Measures and Hermite-Pade Approximants”, J. Comput. Appl. Math., 99:1-2 (1998), 91–103  isi
    10. Hernandez M., Lagomasino G., “Ratio and Relative Asymptotics of Polynomials Orthogonal on an Arc of the Unit Circle”, J. Approx. Theory, 92:2 (1998), 216–244  crossref  mathscinet  zmath  isi
    11. A. I. Aptekarev, “Strong asymptotics of multiply orthogonal polynomials for Nikishin systems”, Sb. Math., 190:5 (1999), 631–669  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    12. Ysern B., Lagomasino G., “Weak Convergence of Varying Measures and Hermite-Pade Orthogonal Polynomials”, Constr. Approx., 15:4 (1999), 553–575  crossref  isi
    13. Van Assche W., Geronimo J.S., Kuijlaars A.B.J., “Riemann–Hilbert problems for multiple orthogonal polynomials”, Special Functions 2000: Current Perspective and Future Directions, Nato Science Series, Series II: Mathematics, Physics and Chemistry, 30, 2001, 23–59  isi
    14. V. N. Sorokin, “Cyclic graphs and Apéry's theorem”, Russian Math. Surveys, 57:3 (2002), 535–571  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    15. A. Branquinho, J. Bustamante, A. Foulquié Moreno, G. López Lagomasino, “Normal indices in Nikishin systems”, Journal of Approximation Theory, 124:2 (2003), 254  crossref
    16. Coussement E., Van Assche W., “Multiple Orthogonal Polynomials Associated with the Modified Bessel Functions of the First Kind”, Constr. Approx., 19:2 (2003), 237–263  crossref  mathscinet  zmath  isi
    17. U. Fidalgo Prieto, J. Illán, G. López Lagomasino, “Hermite–Padé approximation and simultaneous quadrature formulas”, Journal of Approximation Theory, 126:2 (2004), 171  crossref
    18. Ulises Fidalgo Prieto, Guillermo López Lagomasino, “On Perfect Nikishin Systems”, Comput. Methods Funct. Theory, 2:2 (2004), 415  crossref
    19. Prieto U., Lagomasino G., “Rate of Convergence of Generalized Hermite-Pade Approximants of Nikishin Systems”, Constr. Approx., 23:2 (2006), 165–196  crossref  isi
    20. Prieto U.F., Lopez Lagomasino G., “General Results on the Convergence of Multipoint Hermite-Pade Approximants of Nikishin Systems”, Constr. Approx., 25:1 (2007), 89–107  crossref  mathscinet  zmath  isi
    21. Aptekarev, AI, “Asymptotics of Hermite-Pade Rational Approximants for Two Analytic Functions with Separated Pairs of Branch Points (Case of Genus 0)”, International Mathematics Research Papers, 2008, rpm007  mathscinet  zmath  isi
    22. Amílcar Branquinho, Luis Cotrim, Ana Foulquié Moreno, “Matrix interpretation of multiple orthogonality”, Numer Algor, 2009  crossref
    23. Aptekarev A.I., Kalyagin V.A., Saff E.B., “Higher-Order Three-Term Recurrences and Asymptotics of Multiple Orthogonal Polynomials”, Constr. Approx., 30:2 (2009), 175–223  crossref  isi
    24. 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
    25. de la Calle Ysern B., “A Walk through Approximation Theory”, Recent Trends in Orthogonal Polynomials and Approximation Theory, Contemporary Mathematics, 507, 2010, 25–86  crossref  isi
    26. Kuijlaars A.B.J., “Multiple orthogonal polynomial ensembles”, Recent Trends in Orthogonal Polynomials and Approximation Theory, Contemporary Mathematics, 507, 2010, 155–176  crossref  isi
    27. U. Fidalgo Prieto, G. López Lagomasino, “Nikishin systems are perfect. The case of unbounded and touching supports”, Journal of Approximation Theory, 163:6 (2011), 779  crossref
    28. 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
    29. 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
    30. A. P. Starovoitov, “Approksimatsii Ermita–Pade dlya sistemy funktsii Mittag-Lefflera”, PFMT, 2013, no. 1(14), 81–87  mathnet
    31. Filipuk G. Van Assche W. Zhang L., “Ladder Operators and Differential Equations for Multiple Orthogonal Polynomials”, J. Phys. A-Math. Theor., 46:20 (2013), 205204  crossref  zmath  adsnasa  isi
    32. A. P. Starovoitov, “On asymptotic form of the Hermite–Pade approximations for a system of Mittag-Leffler functions”, Russian Math. (Iz. VUZ), 58:9 (2014), 49–56  mathnet  crossref
    33. Lun Zhang, Galina Filipuk, “On Certain Wronskians of Multiple Orthogonal Polynomials”, SIGMA, 10 (2014), 103, 19 pp.  mathnet  crossref
    34. Branquinho A. Fidalgo Prieto U. Foulquie Moreno A., “An Extension of Markov's Theorem”, Proc. Amer. Math. Soc., 142:10 (2014), 3491–3503  isi
    35. G. López Lagomasino, S. Medina Peralta, “On the convergence of type I Hermite–Padé approximants”, Advances in Mathematics, 273 (2015), 124  crossref
    36. G. López Lagomasino, S. Medina Peralta, “On the convergence of type I Hermite–Padé approximants for rational perturbations of a Nikishin system”, Journal of Computational and Applied Mathematics, 2015  crossref
    37. 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
    38. 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
    39. 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  isi
    40. 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
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