| Fourier-Laplace级数的强逼近 |
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| 引用本文： | 张希荣,戴峰. Fourier-Laplace级数的强逼近[J]. 数学进展, 2004, 33(5): 626-630 |
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| 作者姓名： | 张希荣 戴峰 |
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| 作者单位： | 1. 华北电力大学数理系,北京,102206
2. 北京师范大学数学系,北京,100875 |
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| 基金项目： | Project supported by the Natural Science Foundation of China(No. 19971009). |
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| 摘 要： | 设f是Rn(n≥3)中单位球面∑n-1上的可积函数,Sθ(f)是步长为θ∈R的平移算子.σδN(f)是Fourier-Laplace级数的δ阶Ceaaro平均.如果∫π0|Sθ(f)-f|p/θ2dθ∈ L∞ (∑n- 1 ),则∑∞k=0 |σλk(f)-f|p∈L∞(∑n-1)且∑∞k=0(f)-f|p∈L∞(∑n-1),其中Eλk(f)为Cesaro平均σλk的等收敛算子.
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| 关 键 词： | 强逼近 Fourier-Laplace级数 Cesaro平均 等收敛算子 |
Strong Approximation by Fourier-Laplace Series in L∞-norm |
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| Abstract. Strong Approximation by Fourier-Laplace Series in L∞-norm[J]. Advances in Mathematics(China), 2004, 33(5): 626-630 |
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| Authors: | Abstract |
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| Abstract: | Let f be an integrable function on the unit sphere ∑n-1 of Rn (n ≥3) and let Sθ(f) be the translation operator with step θ∈ R. Let σδN (f) be the Cesaro means of order δ of the FourierLaplace series of f. This paper proves that if ∫π0 |Sθ(f)-f|p/θ2dθ∈ L∞ (∑n- 1 ), then ∑∞k=0 | σλk (f) - f |p ∈L∞(∑n-1) and ∑∞k=0 |Eλk(f) - f|p ∈ L∞(∑n-1), where Eλk(f) is the equiconvergent operator of Cesaro means σλk. |
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| Keywords: | strong approximation Fourier-Laplace series Cesaro means equiconvergent operator |
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