| 广义单调序列与Fourier级数的L~1－收敛 |
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| 引用本文： | 褚志仁.广义单调序列与Fourier级数的L~1－收敛[J].汕头大学学报(自然科学版),1996(2). |
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| 作者姓名： | 褚志仁 |
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| 作者单位： | 汕头大学数学系 |
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| 摘 要： | 本文指出：文［４］中的广义单调序列不仅是拟单调序列概念的推广，而且也是Ｏ—正则拟单调序列概念的实质性推广．特别，序列的广义单调性不依赖于Ｏ－正则序列，本文还把文［３］的一个具有Ｏ－正则拟单调系数的Ｆｏｕｒｉｅｒ级数Ｌ１－收敛的充分必要条件推广到具有广义单调系数的Ｆｏｕｒｉｅｒ级数上，所得的结果推广了文［２］和［３］的主要结论．
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| 关 键 词： | O－正则序列 拟单调 广义单调 Fourier级数 L~1－收敛 |
Generalized monotonic sequence and L￣1-convergence of Fourier series |
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| Chu Zhiren.Generalized monotonic sequence and L￣1-convergence of Fourier series[J].Journal of Shantou University(Natural Science Edition),1996(2). |
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| Authors: | Chu Zhiren |
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| Abstract: | In this paper we point out that the generalized monotonic sequence in 4] not only is an extension of quasimonotonicity but also a substantive extension of O-regularly varying quasimonotonicity. It is especially noteworthy that the generalized monotonicity of sequence is independent of O-regularly varying sequence. In this paper, the necessaryand sufficient condition for L1-convergence of Fourier series with O-regularly varying quasimonotonic coefficients in paper 2] is generalized to include Fourier series with generralized monotonic ceofficients, thereby expanding the main conclusions deduced in paper 2] and 3]. |
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| Keywords: | O-regularly varying sequence quasimonotonicity generalized monotonicity Fourier series L￣1-convergence |
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