Hermite-Fejér interpolation for rational systems
Generalized Hermite-type interpolation based on the zeros of the Chebychev polynomial of the first kind for the real rational space \(P_n(a_1, a_2,\dots, a_n)\) was constructed. The non-real elements \(\{a_k\}^n_{k=1}\subset \mathbb{C}\setminus[-1, 1]\) may be paired by complex conjugation and repeated poles. The corresponding generalized Hermite-Fejér interpolation always converges uniformly for every continuous function on \([-1,1]\) provided that the poles stay outside a circle which contains the unit circle in its interior. The uniform approximation of the corresponding Günwald interpolation was characterized. The \(L^p\)-approximation of this Grünwald interpolation always holds for every continuous function on \([-1,1]\).
scientific article; zbMATH DE number 1268077