Equiconvergence of some sequences of complex interpolating rational functions (Q919210)

\textit{E. B. Saff} and \textit{A. Sharma} [Lect. Notes Math. 1105, 256-271 (1984; Zbl 0558.41007)] have proved a generalization to rational functions with denominator \(z^ n-\sigma^ n\), of an equiconvergence result for polynomials, to the effect that rational functions with denominator as above and numerator of degree \(n+m\) interpolating a given function analytic at least in the unit disc in the \(n+m+1st\) roots of unity are very close to rational functions with the same denominator that approximate the given function in \(L^ 2\) on the unit circle. This paper investigates the exact (geometrical) closeness and expresses it in terms of the geometry of the problem.