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Mat. Sb., 2010, Volume 201, Number 10, Pages 137–160 (Mi msb7672)  

This article is cited in 16 scientific papers (total in 16 papers)

On multiple orthogonal polynomials for discrete Meixner measures

V. N. Sorokin

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: The paper examines two examples of multiple orthogonal polynomials generalizing orthogonal polynomials of a discrete variable, meaning thereby the Meixner polynomials. One example is bound up with a discrete Nikishin system, and the other leads to essentially new effects. The limit distribution of the zeros of polynomials is obtained in terms of logarithmic equilibrium potentials and in terms of algebraic curves.
Bibliography: 9 titles.

Keywords: Meixner polynomials, Nikishin systems, Riemann surfaces and algebraic functions, logarithmic equilibrium potentials.

DOI: https://doi.org/10.4213/sm7672

Full text: PDF file (582 kB)
References: PDF file   HTML file

English version:
Sbornik: Mathematics, 2010, 201:10, 1539–1561

Bibliographic databases:

UDC: 517.53
MSC: 42C05
Received: 21.12.2009 and 12.04.2010

Citation: V. N. Sorokin, “On multiple orthogonal polynomials for discrete Meixner measures”, Mat. Sb., 201:10 (2010), 137–160; Sb. Math., 201:10 (2010), 1539–1561

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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. A. I. Aptekarev, D. N. Tulyakov, “Asymptotics of Meixner polynomials and Christoffel-Darboux kernels”, Trans. Moscow Math. Soc., 73 (2012), 67–106  mathnet  crossref  mathscinet  zmath  elib
    2. E. A. Rakhmanov, S. P. Suetin, “Asymptotic behaviour of the Hermite–Padé polynomials of the 1st kind for a pair of functions forming a Nikishin system”, Russian Math. Surveys, 67:5 (2012), 954–956  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    3. Jooste A., Jordaan K., Toókos F., “On the zeros of Meixner polynomials”, Numer. Math., 124:1 (2013), 57–71  crossref  mathscinet  zmath  isi  elib  scopus  scopus  scopus
    4. A. Aptekarev, J. Arvesú, “Asymptotics for multiple Meixner polynomials”, J. Math. Anal. Appl., 411:2 (2014), 485–505  crossref  mathscinet  zmath  isi  elib  scopus
    5. R. K. Kovacheva, S. P. Suetin, “Distribution of zeros of the Hermite–Padé polynomials for a system of three functions, and the Nuttall condenser”, Proc. Steklov Inst. Math., 284 (2014), 168–191  mathnet  crossref  crossref  isi  elib  elib
    6. 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
    7. V. N. Sorokin, “Simultaneous orthogonal polynomials related to Poisson distribution”, Moscow University Mathematics Bulletin, 70:1 (2015), 1–5  mathnet  crossref  mathscinet  isi  elib
    8. V. N. Sorokin, “Ob asimptoticheskikh rezhimakh sovmestnykh mnogochlenov Meiksnera”, Preprinty IPM im. M. V. Keldysha, 2016, 046, 32 pp.  mathnet  crossref
    9. V. G. Lysov, D. N. Tulyakov, “O vektornoi teoretiko-potentsialnoi zadache s matritsei Anzhelesko”, Preprinty IPM im. M. V. Keldysha, 2016, 110, 36 pp.  mathnet  crossref
    10. A. I. Aptekarev, G. López Lagomasino, A. Martínez-Finkelshtein, “On Nikishin systems with discrete components and weak asymptotics of multiple orthogonal polynomials”, Russian Math. Surveys, 72:3 (2017), 389–449  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    11. V. G. Lysov, D. N. Tulyakov, “On a Vector Potential-Theory Equilibrium Problem with the Angelesco Matrix”, Proc. Steklov Inst. Math., 298 (2017), 170–200  mathnet  crossref  crossref  isi  elib
    12. V. N. Sorokin, “On Multiple Orthogonal Polynomials for Three Meixner Measures”, Proc. Steklov Inst. Math., 298 (2017), 294–316  mathnet  crossref  crossref  isi  elib
    13. Driver K., Jooste A., “Interlacing of Zeros of Quasi-Orthogonal Meixner Polynomials”, Quaest. Math., 40:4 (2017), 477–490  crossref  mathscinet  zmath  isi  scopus
    14. V. G. Lysov, D. N. Tulyakov, “On the supports of vector equilibrium measures in the Angelesco problem with nested intervals”, Proc. Steklov Inst. Math., 301 (2018), 180–196  mathnet  crossref  crossref  isi  elib  elib
    15. V. N. Sorokin, “Multipoint Hermite–Padé approximants for three beta functions”, Trans. Moscow Math. Soc., 2018, 117–134  mathnet  crossref  elib
    16. V. N. Sorokin, “Hermite-Padé approximants to the Weyl function and its derivative for discrete measures”, Sb. Math., 211:10 (2020), 1486–1502  mathnet  crossref  crossref
  • Математический сборник Sbornik: Mathematics (from 1967)
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