On Normal Pointsystems of Hermite–Fejér Interpolation of Arbitrary Order Original Research Article

Necessary conditions of normal pointsystems for Hermite–Fejér interpolation of arbitrary (even) order are given. In particular, one of the main results in this paper is: If a pointsystem consists of the zeros of orthogonal polynomials with respect to a weight w on [−1, 1] and is always normal for Hermite–Fejér interpolation of arbitrary (even) order, then w(x)∼(1−x2)−1/2.