关于圆域上Kergin插值的收敛性

本文研究了圆域上Kergin插值算子及其微商对于光滑的被插函数的逼近性能,并考虑了它对古典一元插值法的应用。

SOME RESEARCHES ON WEAK CONVERGENCE OF KERGIN INTERPOLATION

The aim of this paper is to study the weak integral convergence of Kergin interpolation. The results of the weighted integral convergence and the weighted (partial) derivatives integral convergence of Kergin interpolation polynomial for the smooth functions on the unit disk were obtained in the paper. Those generalized Liang's main results were acquired in 1998 to the more extensive situation. At the same time, the estimation of convergence rate of Kergin interpolation polynomial is given by means of introducing a new kind of smooth norm.

多元Stirling数及其性质

本文借用s元的Kergin插值理论以及插值公式定义了一类多元广义Stirling数偶S_1(α,β),S_2(α,β),作为古典Stirling数偶的一种推广。并研究了S_1(α,β),S_2(α,β)的一些性质,如正交性、递推关系、反演公式等。