| 具有分段有界变差系数的三角级数的一个性质 |
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| 引用本文： | 何基龙.具有分段有界变差系数的三角级数的一个性质[J].浙江工程学院学报,2014(1):94-97. |
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| 作者姓名： | 何基龙 |
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| 作者单位： | 浙江理工大学数学研究所,杭州310018 |
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| 摘 要： | 将Leindler定理的条件推广到分段有界变差数列（PBVS）中。当正弦级数的Fourier系数满足分段有界变差条件时，结合最佳逼近的定义，运用分段讨论方法，在坛范数下研究得到正弦级数的最佳逼近与Fourier系数之间的关系式，并对关系式进行了证明。
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| 关 键 词： | 三角级数 分段有界变差数列 Fourier系数 最佳逼近 |
A Property of Trigonometric Series with Piecewise Bounded Variation Coefficients |
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| HE Ji-long.A Property of Trigonometric Series with Piecewise Bounded Variation Coefficients[J].Journal of Zhejiang Institute of Science and Technology,2014(1):94-97. |
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| Authors: | HE Ji-long |
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| Affiliation: | HE Ji-long (Institute of Mathematics, Zhejiang Sci-Tech University, Hangzhou 310018, China) |
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| Abstract: | When Fourier coefficient of sine series meets bounded variation condition, this paper gener- alizes the conditions in Leindler theorem to piecewise bounded variation sequence（PBVS）, obtains the rela- tional expression of optimal approximation and coefficient of sine series through research under LP2k norm with piecewise discussion method in combination with the definition of optimal approximation, and proves the formula. |
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| Keywords: | trigonometric series PBVS（piecewise bounded variation sequence） Fourier coefficient best approximation |
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