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 Algebra i Analiz: Year: Volume: Issue: Page: Find

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

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

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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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
2. A. A. Kononova, “On compact perturbations of finite-zone Jacobi operators”, J. Math. Sci. (N. Y.), 165:4 (2010), 473–482
3. Simanek B., “Asymptotic Properties of Extremal Polynomials Corresponding to Measures Supported on Analytic Regions”, J. Approx. Theory, 170:SI (2013), 172–197
4. Simanek B., “The Bergman Shift Operator on Polynomial Lemniscates”, Constr. Approx., 41:1 (2015), 113–131
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
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