On a Direct Uvarov-Chihara Problem and Some Extensions

K. Castillo (), L. Garza () and F. Marcellán ()
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K. Castillo: Universidade Estadual Paulista – UNESP
L. Garza: Universidad de Colima
F. Marcellán: Universidad Carlos III de Madrid

A chapter in Analytic Number Theory, Approximation Theory, and Special Functions, 2014, pp 691-704 from Springer

Abstract: Abstract In this paper, we analyze a perturbation of a nontrivial probability measure dμ supported on an infinite subset on the real line, which consists on the addition of a time-dependent mass point. For the associated sequence of monic orthogonal polynomials, we study its dynamics with respect to the time parameter. In particular, we determine the time evolution of their zeros in the special case when the measure is semiclassical. We also study the dynamics of the Verblunsky coefficients, i.e., the recurrence relation coefficients of a polynomial sequence, orthogonal with respect to a nontrivial probability measure supported on the unit circle, induced from dμ through the Szegő transformation.

Keywords: Orthogonal Polynomial; Monic Polynomial; Toda Lattice; Spectral Transformation; Toda Hierarchy (search for similar items in EconPapers)
Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4939-0258-3_25

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DOI: 10.1007/978-1-4939-0258-3_25

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