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St. Petersburg Mathematical Journal

ISSN 1547-7371(online) ISSN 1061-0022(print)



On the asymptotics of polynomials orthogonal on a system of curves with respect to a measure with discrete part

Authors: V. A. Kalyagin and A. A. Kononova
Translated by: by the authors
Original publication: Algebra i Analiz, tom 21 (2009), nomer 2.
Journal: St. Petersburg Math. J. 21 (2010), 217-230
MSC (2000): Primary 42C05; Secondary 30D55, 30E15
Published electronically: January 21, 2010
MathSciNet review: 2549452
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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$.

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Additional Information

V. A. Kalyagin
Affiliation: Higher School of Economics, Nizhny Novgorod Branch, Lobachevsky State University, 25/12 Bolshaya Pecherskaya Street, Nizhny Novgorod 603155, Russia

A. A. Kononova
Affiliation: Nizhny Novgorod State Technical University, 24 Minina Street, Nizhny Novgorod 603950, Russia

Keywords: Orthogonal polynomials, strong asymptotics, multivalued functions, Hardy spaces
Received by editor(s): April 15, 2008
Published electronically: January 21, 2010
Additional Notes: The first author was supported in part by Scientific Schools grant 3906.2008.1 and by RFBR grant 08-01-00179
Article copyright: © Copyright 2010 American Mathematical Society

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