论文信息 - On Normal Pointsystems of Hermite-Fejér Interpolation of Arbitrary Order

On Normal Pointsystems of Hermite-Fejér Interpolation of Arbitrary Order

Necessary conditions of normal pointsystems for Hermite-Fejer 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-Fejer interpolation of arbitrary (even) order, then w(x)~(1-x^2)^-^1^/^2.

Ying Guang Shi | Y. Shi

[1] J. Szabados. On the order of magnitude of fundamental polynomials of hermite interpolation , 1993 .

[2] Paul Erdös,et al. On Interpolation. III. Interpolatory Theory of Polynomials , 1940 .

[3] Paul Erdös,et al. On Interpolation II: On the Distribution of the Fundamental Points of Lagrange and Hermite Interpolation , 1938 .

[4] Ying Guang Shi. Bounds and inequalities for general orthogonal polynomials on finite intervals , 1993 .

[5] Weak convergence of orthogonal polynomials , 1994, math/9401209.

[6] V. Totik,et al. Strong and weak convergence of orthogonal polynomials , 1987 .

[7] Ying Guang Shi,et al. On Hermite Interpolation , 2000 .

[8] P. Erdös. On the Uniform Distribution of the Roots of Certain Polynomials , 1942 .