Multipoint Schur algorithm and orthogonal rational functions: convergence properties, I
Classical Analysis and ODEs
2010-02-11 v3 Complex Variables
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.
Cite
@article{arxiv.0812.2050,
title = {Multipoint Schur algorithm and orthogonal rational functions: convergence properties, I},
author = {L. Baratchart and S. Kupin and V. Lunot and M. Olivi},
journal= {arXiv preprint arXiv:0812.2050},
year = {2010}
}
Comments
a preliminary version, 39 pages; some changes in the Introduction, Section 5 (Szeg\H o type asymptotics) is extended