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Algebra i Analiz, 2009, Volume 21, Issue 2, Pages 71–91 (Mi aa1005)  

This article is cited in 5 scientific papers (total in 5 papers)

On the asymptotics of polynomials orthogonal with respect to a measure with atoms on a system of arcs

V. A. Kalyagina, A. A. Kononovab

a Nizhnii Novgorod Branch of the State University "Higher School of Economics", Nizhnii Novgorod, Russia
b Nizhnii Novgorod State Technical University, Nizhnii Novgorod, Russia

Abstract: Consider an absolutely continuous measure on a system of Jordan arcs and (closed) curves in the complex plane, assuming that this measure satisfies the Szegő condition on its support and that the support of the measure is the boundary of some (multiply connected) domain $\Omega$ containing infinity. Adding to the measure a finite number of discrete masses lying in $\Omega$ (off the support of the measure), we study the strong asymptotics of the polynomials orthogonal with respect to the perturbed measure. For this, we solve an extremal problem in a certain class of multivalued functions. Our goal is to give an explicit expression for the strong asymptotics on the support of the perturbed measure, as well as on the domain $\Omega$.

Keywords: orthogonal polynomials, strong asymptotics, multivalued functions, Hardy spaces.

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English version:
St. Petersburg Mathematical Journal, 2010, 21:2, 217–230

Bibliographic databases:

MSC: Primary 42C05; Secondary 30D55, 30E15
Received: 15.04.2008

Citation: V. A. Kalyagin, A. A. Kononova, “On the asymptotics of polynomials orthogonal with respect to a measure with atoms on a system of arcs”, Algebra i Analiz, 21:2 (2009), 71–91; St. Petersburg Math. J., 21:2 (2010), 217–230

Citation in format AMSBIB
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\paper On the asymptotics of polynomials orthogonal with respect to a~measure with atoms on a~system of arcs
\jour Algebra i Analiz
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\pages 71--91
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\pages 217--230
\crossref{https://doi.org/10.1090/S1061-0022-10-01091-5}
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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. V. A. Kalyagin, A. A. Kononova, “On Compact Perturbations of the Limit-Periodic Jacobi Operator”, Math. Notes, 86:6 (2009), 789–800  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    2. A. A. Kononova, “On compact perturbations of finite-zone Jacobi operators”, J. Math. Sci. (N. Y.), 165:4 (2010), 473–482  mathnet  crossref  elib  elib
    3. Simanek B., “Asymptotic Properties of Extremal Polynomials Corresponding to Measures Supported on Analytic Regions”, J. Approx. Theory, 170:SI (2013), 172–197  crossref  mathscinet  zmath  isi  elib  scopus
    4. Simanek B., “The Bergman Shift Operator on Polynomial Lemniscates”, Constr. Approx., 41:1 (2015), 113–131  crossref  mathscinet  zmath  isi  scopus
    5. A. A. Kononova, “On measures generating orthogonal polynomials with similar asymptotic behavior of the ratio at infinity”, Ufa Math. J., 10:1 (2018), 64–75  mathnet  crossref  isi  elib
  • Алгебра и анализ St. Petersburg Mathematical Journal
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