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Mat. Sb., 2011, Volume 202, Number 1, Pages 133–140 (Mi msb7619)  

This article is cited in 19 scientific papers (total in 19 papers)

The asymptotics of Hermite-Padé polynomials for two Markov-type functions

E. A. Rakhmanovab

a Steklov Mathematical Institute, Russian Academy of Sciences
b University of South Florida, Tampa, FL, USA

Abstract: A problem is solved on the limit distribution of the zeros of polynomials which are simultaneously orthogonal on two intervals $\Delta_1$ and $\Delta_2$ of the real line such that $\Delta_1\subset\Delta_2$, under the assumption that the ratio of the weight functions on $\Delta_1$ is a Markov-type function generated by a third interval $\Delta_3$ not intersecting $\overset{\circ}\Delta_2$.
Bibliography: 11 titles.

Keywords: Hermite-Padé approximants, simultaneously orthogonal polynomials, weak asymptotics, vector equilibrium problem.


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English version:
Sbornik: Mathematics, 2011, 202:1, 127–134

Bibliographic databases:

UDC: 517.53
MSC: 41A21, 41A25
Received: 06.08.2009 and 05.08.2010

Citation: E. A. Rakhmanov, “The asymptotics of Hermite-Padé polynomials for two Markov-type functions”, Mat. Sb., 202:1 (2011), 133–140; Sb. Math., 202:1 (2011), 127–134

Citation in format AMSBIB
\by E.~A.~Rakhmanov
\paper The asymptotics of Hermite-Pad\'e polynomials for two Markov-type functions
\jour Mat. Sb.
\yr 2011
\vol 202
\issue 1
\pages 133--140
\jour Sb. Math.
\yr 2011
\vol 202
\issue 1
\pages 127--134

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    This publication is cited in the following articles:
    1. A. A. Gonchar, E. A. Rakhmanov, S. P. Suetin, “Padé–Chebyshev approximants of multivalued analytic functions, variation of equilibrium energy, and the $S$-property of stationary compact sets”, Russian Math. Surveys, 66:6 (2011), 1015–1048  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    2. 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
    3. A. I. Aptekarev, D. N. Tulyakov, “Geometry of Hermite-Padé approximants for system of functions $\{f,f^2\}$ with three branch points”, Preprinty IPM im. M. V. Keldysha, 2012, 077, 25 pp.  mathnet
    4. 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
    5. E. A. Rakhmanov, S. P. Suetin, “The distribution of the zeros of the Hermite-Padé polynomials for a pair of functions forming a Nikishin system”, Sb. Math., 204:9 (2013), 1347–1390  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    6. A. Martínez-Finkelshtein, E. A. Rakhmanov, S. P. Suetin, “A differential equation for Hermite–Padé polynomials”, Russian Math. Surveys, 68:1 (2013), 183–185  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    7. 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
    8. S. P. Suetin, “Distribution of the zeros of Padé polynomials and analytic continuation”, Russian Math. Surveys, 70:5 (2015), 901–951  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    9. A. Martinez-Finkelshtein, E. A. Rakhmanov, S. P. Suetin, “Asymptotics of type I Hermite–Padé polynomials for semiclassical functions”, Modern trends in constructive function theory, Contemp. Math., 661, eds. Hardin D., Lubinsky D., Simanek B., Amer. Math. Soc., Providence, RI, 2016, 199–228  crossref  mathscinet  zmath  isi
    10. A. Martinez-Finkelshtein, E. A. Rakhmanov, Do orthogonal polynomials dream of symmetric curves?, Found. Comput. Math., 16:6 (2016), 1697–1736  crossref  mathscinet  zmath  isi  scopus
    11. A. Martinez-Finkelshtein, G. L. F. Silva, “Critical measures for vector energy: global structure of trajectories of quadratic differentials”, Adv. Math., 302 (2016), 1137–1232  crossref  mathscinet  zmath  isi  scopus
    12. 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
    13. 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
    14. 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
    15. V. G. Lysov, “Ob approksimatsiyakh Ermita–Pade dlya proizvedeniya dvukh logarifmov”, Preprinty IPM im. M. V. Keldysha, 2017, 141, 24 pp.  mathnet  crossref
    16. E. A. Rakhmanov, “Zero distribution for Angelesco Hermite–Padé polynomials”, Russian Math. Surveys, 73:3 (2018), 457–518  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    17. 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
    18. S. P. Suetin, “On an Example of the Nikishin System”, Math. Notes, 104:6 (2018), 905–914  mathnet  crossref  crossref  mathscinet  isi  elib
    19. Martinez-Finkelshtein A. Silva G.L.F., “Critical Measures For Vector Energy: Asymptotics of Non-Diagonal Multiple Orthogonal Polynomials For a Cubic Weight”, Adv. Math., 349 (2019), 246–315  crossref  mathscinet  zmath  isi
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