Abstract
Classical Schur analysis is intimately related to the theory of orthogonal polynomials on the circle. We investigate 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 Szegő theory in the case that interpolation points may accumulate on the unit circle. This leads to a generalization of results in [22, 10], and new types of asymptotics.
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