| 小波级数的部分和的一致收敛性 |
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| 引用本文： | 赵书改,曹怀信.小波级数的部分和的一致收敛性[J].兰州理工大学学报,2012,38(2):146-149. |
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| 作者姓名： | 赵书改 曹怀信 |
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| 作者单位： | 1. 咸阳师范学院 数学与信息科学学院,陕西咸阳,712000
2. 陕西师范大学 数学与信息科学学院,陕西西安,710062 |
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| 基金项目： | 本文得到咸阳师范学院专项科研基金资助项目 |
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| 摘 要： | 讨论小波级数的部分和的一致收敛性.通过引入函数空间Lr2(R),研究f∈Lr2(R)的r阶导数fm(r)的小波级数的部分和fm(r)对f(r)的一致逼近问题.当f(r)在(a,b)上连续时,建立fm(r)逼近于f(r)的速度的一个精确估计,进而得到相关的一致收敛的结论.
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| 关 键 词： | 小波级数 部分和 一致收敛性 尺度函数 |
Uniform convergence of partial sum of wavelet expansions |
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| ZHAO Shu-gai
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CAO Huai-xin.Uniform convergence of partial sum of wavelet expansions[J].Journal of Lanzhou University of Technology,2012,38(2):146-149. |
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| Authors: | ZHAO Shu-gai CAO Huai-xin |
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| Institution: | 1.Institute of Mathematics and Information Science,Xianyang Normal University,Xianyang 712000;2.Institute of Mathematics and Information Science,Shaanxi Normal University,Xi’an 710062) |
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| Abstract: | The uniform convergence of the partial sum of wavelet expansions was discussed.By introducing a functional space L2r(R),the problem of uniform approximation of partial sum f(r)m of wavelet expansions of its r-th derivative f(r) to f(r) was studied.If f(r) were continuous on(a,b),an exact estimation of approximation rate of f(r)m to f(r) would be established,so that the result of related uniform convergence would be obtained. |
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| Keywords: | wavelet expansion partial sum uniform convergence scale function |
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