二重Fourier级数的平行六边形求和法

J4 ›› 2011, Vol. 49 ›› Issue (06): 973-978.

二重Fourier级数的平行六边形求和法

王淑云¹, 钱李新¹, 孙雪楠², 梁学章³, 沈卫平¹

1. 浙江师范大学数理与信息工程学院, 浙江金华 321004；2. 东北师范大学数学与统计学院, 长春 130024； 3. 吉林大学数学学院, 长春 130012

收稿日期:2010-12-29 出版日期:2011-11-26 发布日期:2011-11-28
通讯作者: 王淑云 E-mail:wshy888@yahoo.com.cn

Parallel Hexagon’s Summation Methods ofDouble Fourier Series of Functions

WANG Shuyun¹, QIAN Lixin¹, SUN Xuenan², LIANG Xuezhang³, SHEN Weiping¹

1. College of Mathematics Physics and Information Engineering, Zhejiang Normal University, Jinhua 321004,Zhejiang Province, China|2. School of Mathematics and Statistics, Northeast Normal University, Changchun 130024, China|3. College of Mathematics, Jilin University, Changchun 130012, China

Received:2010-12-29 Online:2011-11-26 Published:2011-11-28
Contact: WANG Shuyun E-mail:wshy888@yahoo.com.cn

摘要/Abstract

摘要：

将线性求和法应用于三向剖分平行六边形域上二重Fourier级数的平行六边形截断, 提出一种平行六边形求和法. 通过构造一个新的收敛因子得到一个积分算子, 并证明了该积分算子对于以平行六边形域为周期的二元连续函数的一致收敛性.

关键词: 平行六边形求和法；收敛因子；三向坐标；一致收敛

Abstract:

Linear summation method was applied to the truncations on parallel hexagon of double Fourier series associating with threedirectional coordinates. The parallel hexagon’s summation of double Fourier series of a function was putted forward. A specific convergence factor was constructed. A linear integral operator with the convergence factor was obtained. It has been proved that
the operator converges uniformly to any given continuous double function with periodic domain Ω, where Ω is a parallel hexagon domain.

Key words: parallel hexagonal summation, convergence factor, threedirection coordinate, uniform convergence

中图分类号:

O174.21

王淑云, 钱李新, 孙雪楠, 梁学章, 沈卫平. 二重Fourier级数的平行六边形求和法[J]. J4, 2011, 49(06): 973-978.

WANG Chu-Yun, JIAN Li-Xin, SUN Xue-Nan, LIANG Hua-Zhang, CHEN Wei-Beng. Parallel Hexagon’s Summation Methods ofDouble Fourier Series of Functions[J]. J4, 2011, 49(06): 973-978.