Matematicheskii Sbornik
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Subscription
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Mat. Sb.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Mat. Sb., 1999, Volume 190, Number 5, Pages 3–44 (Mi msb401)  

This article is cited in 49 scientific papers (total in 50 papers)

Strong asymptotics of multiply orthogonal polynomials for Nikishin systems

A. I. Aptekarev

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

Abstract: Strong asymptotic formulae for the Hermite–Padé polynomials for systems of Markov-type functions in the Nikishin class are obtained. The proof is based on the properties of certain rational functions on Riemann surfaces associated with the supports of the measures generating the Nikishin system.

DOI: https://doi.org/10.4213/sm401

Full text: PDF file (471 kB)
References: PDF file   HTML file

English version:
Sbornik: Mathematics, 1999, 190:5, 631–669

Bibliographic databases:

UDC: 517.5
MSC: Primary 42C05, 33C25; Secondary 41A21
Received: 02.02.1998 and 28.09.1998

Citation: A. I. Aptekarev, “Strong asymptotics of multiply orthogonal polynomials for Nikishin systems”, Mat. Sb., 190:5 (1999), 3–44; Sb. Math., 190:5 (1999), 631–669

Citation in format AMSBIB
\Bibitem{Apt99}
\by A.~I.~Aptekarev
\paper Strong asymptotics of multiply orthogonal polynomials for Nikishin systems
\jour Mat. Sb.
\yr 1999
\vol 190
\issue 5
\pages 3--44
\mathnet{http://mi.mathnet.ru/msb401}
\crossref{https://doi.org/10.4213/sm401}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1702555}
\zmath{https://zbmath.org/?q=an:0957.42015}
\elib{https://elibrary.ru/item.asp?id=13312364}
\transl
\jour Sb. Math.
\yr 1999
\vol 190
\issue 5
\pages 631--669
\crossref{https://doi.org/10.1070/sm1999v190n05ABEH000401}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000083433500001}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-0033478870}


Linking options:
  • http://mi.mathnet.ru/eng/msb401
  • https://doi.org/10.4213/sm401
  • http://mi.mathnet.ru/eng/msb/v190/i5/p3

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    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. Aptekarev, AI, “Multiple orthogonal polynomials”, Journal of Computational and Applied Mathematics, 99:1–2 (1998), 423  crossref  mathscinet  zmath  isi  elib  scopus  scopus  scopus
    2. 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  mathscinet  zmath  isi
    3. 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
    4. A. I. Aptekarev, “Sharp constants for rational approximations of analytic functions”, Sb. Math., 193:1 (2002), 1–72  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    5. 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
    6. M. A. Lapik, “Support of the extremal measure in a vector equilibrium problem”, Sb. Math., 197:8 (2006), 1205–1221  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    7. Aptekarev, AI, “On the limit behavior of recurrence coefficients for multiple orthogonal polynomials”, Journal of Approximation Theory, 139:1–2 (2006), 346  crossref  mathscinet  zmath  isi  elib  scopus  scopus  scopus
    8. Enolskii V., Grava T., “Riemann–Hilbert problem and algebraic curves”, Bilinear Integrable Systems: From Classical to Quatum, Continuous to Discrete, Nato Science Series, Series II: Mathematics, Physics and Chemistry, 201, 2006, 65–76  mathscinet  zmath  isi
    9. 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  elib
    10. Lysov, V, “Strong asymptotics for multiple laguerre polynomials”, Constructive Approximation, 28:1 (2008), 61  crossref  mathscinet  zmath  isi  elib  scopus  scopus  scopus
    11. Aptekarev, AI, “Asymptotics of Hermite-Pade Approximants for Two Functions with Branch Points”, Doklady Mathematics, 78:2 (2008), 717  mathnet  crossref  mathscinet  zmath  isi  elib  scopus  scopus  scopus
    12. Balogh, F, “Regularity of a vector potential problem and its spectral curve”, Journal of Approximation Theory, 161:1 (2009), 353  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    13. Aptekarev, AI, “Higher-Order Three-Term Recurrences and Asymptotics of Multiple Orthogonal Polynomials”, Constructive Approximation, 30:2 (2009), 175  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    14. 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
    15. Lopez Lagomasino G., Rocha I.A., “A canonical family of multiple orthogonal polynomials for Nikishin systems”, Journal of Mathematical Analysis and Applications, 372:2 (2010), 390–401  crossref  mathscinet  zmath  isi  elib  scopus  scopus  scopus
    16. 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  mathscinet  zmath  isi
    17. Kuijlaars A.B.J., “Multiple orthogonal polynomial ensembles”, Recent Trends in Orthogonal Polynomials and Approximation Theory, Contemporary Mathematics, 507, 2010, 155–176  crossref  mathscinet  zmath  isi
    18. A. López García, “Asymptotics of multiple orthogonal polynomials for a system of two measures supported on a starlike set”, Journal of Approximation Theory, 2011  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    19. 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
    20. 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
    21. Fidalgo Prieto U., Lopez Lagomasino G., “Nikishin Systems Are Perfect”, Constr Approx, 34:3 (2011), 297–356  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    22. Beckermann B., Kalyagin V., Matos A.C., Wielonsky F., “How Well Does the Hermite-Pade Approximation Smooth the Gibbs Phenomenon?”, Math Comp, 80:274 (2011), 931–958  crossref  mathscinet  zmath  isi  elib  scopus  scopus  scopus
    23. Duits M., Kuijlaars A.B.J., Mo M.Yu., “The Hermitian Two Matrix Model with an Even Quartic Potential”, Mem. Am. Math. Soc., 217:1022 (2012), 1+  crossref  mathscinet  isi  elib  scopus  scopus  scopus
    24. 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
    25. A. P. Starovoitov, “Approksimatsii Ermita–Pade dlya sistemy funktsii Mittag-Lefflera”, PFMT, 2013, no. 1(14), 81–87  mathnet
    26. 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  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus
    27. 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
    28. Lun Zhang, Galina Filipuk, “On Certain Wronskians of Multiple Orthogonal Polynomials”, SIGMA, 10 (2014), 103, 19 pp.  mathnet  crossref
    29. 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
    30. A. I. Aptekarev, A. I. Bogolyubskii, “Matrichnaya zadacha Rimana–Gilberta dlya approksimatsii Pade po ortogonalnym razlozheniyam”, Preprinty IPM im. M. V. Keldysha, 2014, 103, 16 pp.  mathnet
    31. 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  scopus  scopus  scopus
    32. 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
    33. 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
    34. M. A. Lapik, “Ekstremalnyi funktsional dlya vektornykh zadach ravnovesiya logarifmicheskogo potentsiala vo vneshnem pole s matritsei vzaimodeistviya Anzhelesko”, Preprinty IPM im. M. V. Keldysha, 2015, 083, 23 pp.  mathnet
    35. 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
    36. 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
    37. Fidalgo U., “Convergent interpolatory quadrature schemes”, Appl. Numer. Math., 111 (2017), 111–143  crossref  mathscinet  zmath  isi  scopus
    38. A. I. Aptekarev, A. I. Bogolyubskii, M. Yattselev, “Convergence of ray sequences of Frobenius-Padé approximants”, Sb. Math., 208:3 (2017), 313–334  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    39. Aptekarev A.I., Van Assche W., Yattselev M.L., “Hermite-Padé Approximants for a Pair of Cauchy Transforms with Overlapping Symmetric Supports”, Commun. Pure Appl. Math., 70:3 (2017), 444–510  crossref  mathscinet  zmath  isi  scopus
    40. 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
    41. V. G. Lysov, “Ob approksimatsiyakh Ermita–Pade dlya proizvedeniya dvukh logarifmov”, Preprinty IPM im. M. V. Keldysha, 2017, 141, 24 pp.  mathnet  crossref
    42. 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  scopus  scopus  scopus
    43. 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
    44. 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
    45. 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
    46. M. A. Lapik, D. N. Tulyakov, “Vektornye zadachi ravnovesiya Anzhelesko i Nikishina i mnogomernyi analog tsepochki Tody. Predelnyi sluchai, kogda vtoroi otrezok styanut v tochku”, Preprinty IPM im. M. V. Keldysha, 2018, 275, 12 pp.  mathnet  crossref  elib
    47. 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
    48. 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
    49. Bosuwan N., “On Row Sequences of Hermite-Pade Approximation and Its Generalizations”, Mathematics, 8:3 (2020)  crossref  isi
    50. A. I. Aptekarev, “Slabye i silnye asimptotiki ortogonalnykh mnogochlenov c «peremennym» vesom”, Posvyaschaetsya 70-letiyu prezidenta RUDN V.M. Filippova, SMFN, 67, no. 3, Rossiiskii universitet druzhby narodov, M., 2021, 427–441  mathnet  crossref
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
    Number of views:
    This page:501
    Full text:200
    References:38
    First page:3

     
    Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2021