An interpolation process with Hermite-Fejér boundary conditions on the unit circle

This research article seeks to rigorously examine the approximation achieved through interpolation with Hermite-Fejér boundary conditions on the unit circle. The nodal system is comprised of the vertically projected zeros of the Jacobi polynomial onto the unit circle, with boundary points at ±1. Additionally, convergence is demonstrated by analyzing analytic functions within a suitable domain, supported by various numerical experiments.