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Asymptotic behaviour of Verblunsky coefficients |
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| Authors: | María Pilar Alfaro Manuel Bello Hernández Jesús María Montaner |
| Institution: | a Departamento de Matemáticas, Universidad de Zaragoza, Calle Pedro Cerbuna s/n, 50009 Zaragoza, Spain b Departamento de Matemáticas y Computación, Universidad de La Rioja, Edificio J. L. Vives, Calle Luis de Ulloa s/n, 26004 Logroño, Spain c Departamento de Matemática Aplicada, Universidad de Zaragoza, Edificio Torres Quevedo, Calle María de Luna 3, 50018 Zaragoza, Spain |
| Abstract: | Let  , ζh≠ζk, h≠k and |ζj|=1, j=1,…,m, and consider the polynomials orthogonal with respect to  ,  , where μ is a finite positive Borel measure on the unit circle with infinite points in its support, such that the reciprocal of its Szeg? function has an analytic extension beyond |z|<1. In this paper we deduce the asymptotic behaviour of their Verblunsky coefficients. By means of this result, an asymptotic representation for these polynomials inside the unit circle is also obtained. |
| Keywords: | Orthogonal polynomials Verblunsky coefficients |
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