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Mat. Sb. (N.S.), 1985, Volume 128(170), Number 2(10), Pages 216–229 (Mi msb2124)  

This article is cited in 30 scientific papers (total in 30 papers)

On the asymptotics of the ratio of orthogonal polynomials and convergence of multipoint Padé approximants

G. L. Lopes


Abstract: A theorem is proved on the asymptotics of the ratio of polynomials orthogonal with respect to varying weights (that depend on the degree of the polynomial).
Bibliography: 10 titles.

Full text: PDF file (616 kB)
References: PDF file   HTML file

English version:
Mathematics of the USSR-Sbornik, 1987, 56:1, 207–219

Bibliographic databases:

UDC: 517.53
MSC: 30E10, 33A65
Received: 07.09.1984

Citation: G. L. Lopes, “On the asymptotics of the ratio of orthogonal polynomials and convergence of multipoint Padé approximants”, Mat. Sb. (N.S.), 128(170):2(10) (1985), 216–229; Math. USSR-Sb., 56:1 (1987), 207–219

Citation in format AMSBIB
\Bibitem{Lop85}
\by G.~L.~Lopes
\paper On the asymptotics of the ratio of orthogonal polynomials and convergence of multipoint Pad\'e approximants
\jour Mat. Sb. (N.S.)
\yr 1985
\vol 128(170)
\issue 2(10)
\pages 216--229
\mathnet{http://mi.mathnet.ru/msb2124}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=809486}
\zmath{https://zbmath.org/?q=an:0604.30044}
\transl
\jour Math. USSR-Sb.
\yr 1987
\vol 56
\issue 1
\pages 207--219
\crossref{https://doi.org/10.1070/SM1987v056n01ABEH003032}


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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. E. A. Rakhmanov, “On asymptotic properties of polynomials orthogonal on the circle with weights not satisfying the Szegö's condition”, Math. USSR-Sb., 58:1 (1987), 149–167  mathnet  crossref  mathscinet  zmath
    2. Nevai P., “Freud,Geza, Orthogonal Polynomials and Christoffel Functions - a Case-Study”, J. Approx. Theory, 48:1 (1986), 3–167  crossref  mathscinet  zmath  isi
    3. Nevai P., “Orthogonal Polynomials, Measures and Recurrences on the Unit-Circle”, Trans. Am. Math. Soc., 300:1 (1987), 175–189  crossref  mathscinet  zmath  isi
    4. A. I. Aptekarev, “Asymptotics of simultaneously orthogonal polynomials in the Angelesco case”, Math. USSR-Sb., 64:1 (1989), 57–84  mathnet  crossref  mathscinet  zmath  isi
    5. G. L. Lopes, “Convergence of Padé approximants of Stieltjes type meromorphic functions and comparative asymptotics for orthogonal polynomials”, Math. USSR-Sb., 64:1 (1989), 207–227  mathnet  crossref  mathscinet  zmath
    6. G. L. Lopes, “Relative asymptotics for polynomials orthogonal on the real axis”, Math. USSR-Sb., 65:2 (1990), 505–529  mathnet  crossref  mathscinet  zmath
    7. Herrera R. Lagomasino G., “Relative Asymptotics of Orthogonal Polynomials with Respect to Varying Measures .2.”, Lect. Notes Math., 1354 (1988), 140–154  crossref  zmath  isi
    8. Lopez G. Rakhmanov E., “Rational-Approximations, Orthogonal Polynomials and Equilibrium Distributions”, Lect. Notes Math., 1329 (1988), 125–157  crossref  mathscinet  zmath  isi
    9. Knopfmacher A., Lubinsky D., Nevai P., “Freud Conjecture and Approximation of Reciprocals of Weights by Polynomials”, Constr. Approx., 4:1 (1988), 9–20  crossref  mathscinet  zmath  isi
    10. Nevai P., “Characterization of Measures Associated with Orthogonal Polynomials on the Unit-Circle”, Rocky Mt. J. Math., 19:1 (1989), 293–302  crossref  mathscinet  zmath  isi
    11. Lagomasino G., “Asymptotics of Polynomials Orthogonal with Respect to Varying Measures”, Constr. Approx., 5:2 (1989), 199–219  crossref  mathscinet  zmath  isi
    12. Adhemar Bultheel, Pablo González-Vera, Erik Hendriksen, Olav Njåstad, “The computation of orthogonal rational functions and their interpolating properties”, Numer Algor, 2:1 (1992), 85  crossref  mathscinet  zmath
    13. Pan K., “On the Convergence of the Rational Interpolation Approximant of Caratheodory Functions”, J. Comput. Appl. Math., 54:3 (1994), 371–376  crossref  mathscinet  zmath  isi
    14. Lagomasino G. Finkelshtein A., “Rate of Convergence of 2-Point Pade Approximants and Logarithmic Asymptotics of Laurent-Type Orthogonal Polynomials”, Constr. Approx., 11:2 (1995), 255–286  crossref  mathscinet  zmath  isi
    15. A. Bultheel, C. Díaz-Mendoza, P. González-Vera, R. Orive, “Quadrature on the half line and two-point Padé approximants to Stieltjes functions. Part III. The unbounded case”, Journal of Computational and Applied Mathematics, 87:1 (1997), 95  crossref
    16. Totik V., “Orthogonal Polynomials with Respect to Varying Weights”, J. Comput. Appl. Math., 99:1-2 (1998), 373–385  crossref  mathscinet  zmath  isi
    17. 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
    18. 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
    19. Ysern, BD, “Weak convergence of varying measures and Hermite-Pade orthogonal polynomials”, Constructive Approximation, 15:4 (1999), 553  crossref  isi  elib
    20. Lubinsky, DS, “Asymptotics of orthogonal polynomials: Some old, some new, some identities”, Acta Applicandae Mathematicae, 61:1–3 (2000), 207  crossref  isi  elib
    21. Baratchart L., Stahl H., Wielonsky F., “Asymptotic Error Estimates for l-2 Best Rational Approximants to Markov Functions”, J. Approx. Theory, 108:1 (2001), 53–96  crossref  mathscinet  zmath  isi
    22. J. Van Deun, A. Bultheel, “Ratio asymptotics for orthogonal rational functions on an interval”, Journal of Approximation Theory, 123:2 (2003), 162  crossref
    23. A. I. Aptekarev, G. López Lagomasino, I. Alvarez Rocha, “Ratio asymptotics of Hermite–Padé polynomials for Nikishin systems”, Sb. Math., 196:8 (2005), 1089–1107  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    24. Bultheel A., Gonzalez-Vera P., Hendriksen E., Njastad O., “Orthogonal Rational Functions on the Unit Circle: From the Scalar to the Matrix Case”, Orthogonal Polynomials and Special Functions: Computation and Applications, Lect. Notes Math., 1883, eds. Marcellan F., VanAssche W., Springer-Verlag Berlin, 2006, 187–228  crossref  mathscinet  isi
    25. Garcia, AL, “Ratio asymptotic of Hermite-Pade orthogonal polynomials for Nikishin systems. II”, Advances in Mathematics, 218:4 (2008), 1081  crossref  isi
    26. Adhemar Bultheel, Leyla Daruis, Pablo González-Vera, “Quadrature formulas on the unit circle with prescribed nodes and maximal domain of validity”, Journal of Computational and Applied Mathematics, 231:2 (2009), 948  crossref
    27. U. Fidalgo Prieto, A. López García, G. López Lagomasino, V. N. Sorokin, “Mixed Type Multiple Orthogonal Polynomials for Two Nikishin Systems”, Constr Approx, 2010  crossref
    28. 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
    29. A. I. Aptekarev, V. I. Buslaev, A. Martínez-Finkelshtein, S. P. Suetin, “Padé approximants, continued fractions, and orthogonal polynomials”, Russian Math. Surveys, 66:6 (2011), 1049–1131  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    30. A. I. Bogolyubskii, “Strong Asymptotics of Diagonal Frobenius–Padé Approximants and Nikishin Systems”, Math. Notes, 99:6 (2016), 938–941  mathnet  crossref  crossref  mathscinet  isi  elib
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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