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Multipoint Schur algorithm and orthogonal rational functions: convergence properties, I

Abstract : Classical Schur analysis is intimately connected to the theory of orthogonal polynomials on the circle [Simon, 2005]. We investigate here the connection between multipoint Schur analysis and orthogonal rational functions. Specifically, we study the convergence of the Wall rational functions via the development of a rational analogue to the Szeg\H o theory, in the case where the interpolation points may accumulate on the unit circle. This leads us to generalize results from [Khrushchev,2001], [Bultheel et al., 1999], and yields asymptotics of a novel type.
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https://hal.inria.fr/hal-00764820
Contributor : Martine Olivi <>
Submitted on : Monday, February 18, 2013 - 11:10:08 AM
Last modification on : Friday, December 20, 2019 - 4:08:02 PM

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Laurent Baratchart, Stanislas Kupin, V. Lunot, Martine Olivi. Multipoint Schur algorithm and orthogonal rational functions: convergence properties, I. Journal d'analyse mathématique, Springer, 2011, 114, pp.207-253. ⟨10.1007/s11854-011-0016-9⟩. ⟨hal-00764820⟩

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