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Journal Articles Journal d'analyse mathématique Year : 2011

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.

Dates and versions

hal-00764820 , version 1 (18-02-2013)

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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, 2011, 114, 1, pp.207-253. ⟨10.1007/s11854-011-0016-9⟩. ⟨hal-00764820⟩
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