Hermite and Hermite-Fejér interpolation at Pollaczek zeros

In order to approximate functions defined on $(-1,1)$ which can grow exponentially at $\pm 1$, we introduce an Hermite and an Hermite–Fejér-type interpolation process based at Pollaczek-type zeros. We prove the convergence of these processes in weighted uniform and $L^p$ norms and provide error estimates which are comparable with the best weighted approximation in suitable function spaces.