On the divergence phenomenon in Hermite-Fejér interpolation (Q1841218)

Generalizing results of \textit{L. Brutman} and \textit{I. Gopengauz} [Constructive Approximation 15, 611-617 (1999; Zbl 0939.41005)], we show that for any nonconstant entire function \(f\) and any interpolation scheme on \([-1,1]\), the associated Hermite-Fejér interpolating polynomials diverge on any infinite subset of \(\mathbb{C}\setminus [-1,1]\). Moreover, it turns out that even for the locally uniform convergence on the open interval \(]-1,1[\) it is necessary that the interpolation scheme converges to the arcsine distribution.