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

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

2008-12-10

arxiv.org/abs/0812.2050v3

Mathematics

Classical Analysis and ODEs

a preliminary version, 39 pages; some changes in the Introduction, Section 5 (Szeg\H o type asymptotics) is extended

Scientific paper

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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