一种Cauchy型主值积分的求积公式的一致收敛性

数学物理学报

一种Cauchy型主值积分的求积公式的一致收敛性

蔡好涛;

曲阜师范大学数学科学学院山东曲阜 273165;

中国科学院数学与系统科学研究院北京 100080

收稿日期:2004-03-30 修回日期:2005-04-10
通讯作者: 蔡好涛
基金资助:
国家自然科学基金(No.1022002)

On the Uniform Convergence of a Kind Quadrature Rule for

Cauchy Type Singular Integrals

Cai Haotao;

Department of Mathematics, Qufu Normal University, Qufu 273165;

Academy of Mathematics and Systems Sciences, Chinese Academy of Sciences, Beijing 100080

Received:2004-03-30 Revised:2005-04-10
Contact: Cai Haotao

摘要/Abstract

摘要： 该文首先给出Cauchy型主值积分φ(wf,x)的一种求积公式φ_m^*(wf,x),然后证明序列$φ_m^*(wf,x)}_m=2^∞在整个闭区间[-1,1]上是一致收敛到Cauchy型主值积分φ(wf,x)的,同时给出它的误差界.

关键词: Cauchy型主值积分, Dini条件, 广义Jacobi权函数

Abstract: In this paper, the author first gives a kind quadrature rule $\Phi_m^{*}(wf,x)$ for Cauchy type singular integral $\Phi(wf,x)$, then proves the sequence $\{\Phi_m^{*}(wf,x)\}_{m=2}^{\infty}$ is uniformly convergent to $\Phi(wf,x)$ on the interval $[-1,1]$, at that time gives its error bounds.

Key words: Cauchy type singular integral, Dini conditions, Generalized Jacobi weight.

中图分类号:

45E10

蔡好涛;. 一种Cauchy型主值积分的求积公式的一致收敛性[J]. 数学物理学报, 2006, 26(3): 421-425.

Cai Haotao;.

On the Uniform Convergence of a Kind Quadrature Rule for

Cauchy Type Singular Integrals

[J]. Acta mathematica scientia,Series A, 2006, 26(3): 421-425.