Interpolation by rational functions with nodes on the unit circle
In this paper, the authors consider the convergence of the sequence of rational interpolations to a function \(f(z)\) which is analytic on the open unit disk and continuous in its closure. The interpolation functions have preassigned poles and the interpolation nodes are zeros of certain para-orthogonal functions with respect to a given absolutely continuous measure \(\mu\) on the unit circle. If \(\mu\) is the Lebesgue measure, the zeroes of the corresponding para-orthogonal polynomials are the roots of unity, which leads to the interpolation problem studied in \textit{J. L. Walsh} and \textit{A. Sharma} [Pac. J. Math. 14, 727-730 (1964; Zbl 0192.16802)].
scientific article; zbMATH DE number 1546741