| 二重Fourier级数的平行六边形求和法 |
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| 引用本文： | 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].吉林大学学报(理学版),2011,49(6):973-978. |
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| 作者姓名： | 王淑云 钱李新 孙雪楠 梁学章 沈卫平 |
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| 作者单位： | 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 |
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| 基金项目： | 国家自然科学基金(批准号:60773098); 浙江省自然科学基金(批准号:Y6100375) |
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| 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.
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| 关 键 词： | 平行六边形求和法 收敛因子 三向坐标 一致收敛 |
| 收稿时间： | 2010-12-29 |
Parallel Hexagon's Summation Methods of Double Fourier Series of Functions |
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| WANG Shu-yun,QIAN Li-xin,SUN Xue-nan,LIANG Xue-zhang,SHEN Wei-ping.Parallel Hexagon's Summation Methods of Double Fourier Series of Functions[J].Journal of Jilin University: Sci Ed,2011,49(6):973-978. |
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| Authors: | WANG Shu-yun QIAN Li-xin SUN Xue-nan LIANG Xue-zhang SHEN Wei-ping |
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| Institution: | 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 |
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| Abstract: | Linear summation method was applied to the truncations on parallel hexagon of double Fourier series associating with three directionalcoordinates. 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. |
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| Keywords: | parallel hexagonal summation convergence factor three-direction coordinate uniform convergence |
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