多点Schur算法与正交有理函数：收敛性，I
Multipoint Schur algorithm and orthogonal rational functions: convergence properties, I
摘要：
经典舒尔分析与圆上的正交多项式理论密切相关[Simon，2005]。我们在这里调查多点舒尔分析和正交有理函数之间的联系。具体而言，我们研究了收敛的壁有理函数通过发展一个合理的模拟Szeg \H o理论，在这种情况下，插值点可能会积累在单位圆。这导致我们推广[Khrushchev，2001]，[Bultheel et al.，1999]，并产生一种新的类型的渐近。
英文摘要：
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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