Hermite插值与Jacobi展开在过收敛方面的关系

北京大学学报（自然科学版）

Hermite插值与Jacobi展开在过收敛方面的关系

娄元仁

北京大学数学科学学院，北京，100871

收稿日期:1998-09-25 出版日期:1999-09-20 发布日期:1999-09-20

The Relations between the Hermite Interpolant and Jacobi Expansion on Equiconvergenc

LOU Yuanren

School of Mathematical Sciences, Peking University, Beijing, 100871

Received:1998-09-25 Online:1999-09-20 Published:1999-09-20

摘要/Abstract

摘要： 对纽线内部的解析函数，得到了Hermite插值与Jacobi多项式之差的过收敛性的精确估计；此外还指出有关的差在过收敛区域的边界上一致收敛的充分必要条件。

关键词: Jacobi展开, Hermite插值, 过收敛性

Abstract: A quantitative estimates in the theory of equiconvergence of differences between the Hermite interpolant and Jacobi polynomials is obtained for functions analylic inside lemniscate. A necessary and sufficient condition that the related difference converges uniformly to zero on the boundary of the equiconvergence area is also showed.

Key words: Jacobi expansion, Hermite interpolant, equiconvergence

中图分类号:

娄元仁. Hermite插值与Jacobi展开在过收敛方面的关系[J]. 北京大学学报（自然科学版）.

LOU Yuanren. The Relations between the Hermite Interpolant and Jacobi Expansion on Equiconvergenc[J]. Acta Scientiarum Naturalium Universitatis Pekinensis.

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https://xbna.pku.edu.cn/CN/Y1999/V35/I5/602