高维小波展开式的一致收敛性

J4 ›› 2010, Vol. 45 ›› Issue (10): 89-92.

高维小波展开式的一致收敛性

赵书改1,曹怀信2*

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

收稿日期:2009-05-08 出版日期:2010-10-16 发布日期:2010-10-19
通讯作者: 曹怀信(1958-),男,博士,教授,研究方向为算子理论与小波分析.
作者简介:赵书改(1981-),女,硕士,讲师,研究方向为算子理论与小波分析.Email: zhaosg1981@163. com
基金资助:
国家自然科学基金资助项目(10571113)

Uniform convergence of high-dimensional wavelet expansions

ZHAO Shu-gai 1, CAO Huai-xin2*

1. College of Mathematics and Information Science, Xianyang Normal University, Xianyang 712000, Shaanxi, China;
2. College of Mathematics and Information Science, Shaanxi Normal University, Xi’an 710062, Shaanxi, China

Received:2009-05-08 Online:2010-10-16 Published:2010-10-19

摘要/Abstract

摘要：

研究高维小波展开式的部分和的一致收敛性。建立当m→-∞时高维小波展开式的一致收敛定理; 其次,通过引入拟正δ序列的概念,构造一个一致逼近序列并得到该序列的逐点收敛性;最后,通过证明多分辨分析的再生核序列｛q_m｝_m∈Z是一个拟正δ序列,建立当m→+∞时高维小波展开式的一致收敛定理。

关键词: 高维小波展开式;一致收敛性;拟正δ序列

Abstract:

Uniform convergence of high-dimensional wavelet expansions is discussed. First, a uniform convergence theorem on high-dimensional wavelet expansion is established when m→-∞.Then, by introducing the concept of a quasi-positive δ sequence, a uniformly convergent sequence is constructed and its pointwise convergence is obtained. Finally, it is proved that the reproducing kernel sequence ｛q_m｝_m∈Z of a multiresolution analysis on certain conditions is a quasi-positive δ sequence, and a uniform convergence theorem on high-dimensional wavelet expansion is given when m→+∞.

Key words: high-dimensional wavelet expansion; uniform convergence; quasi-positive δ sequence

赵书改1,曹怀信2*. 高维小波展开式的一致收敛性[J]. J4, 2010, 45(10): 89-92.

ZHAO Shu-gai 1, CAO Huai-xin2*. Uniform convergence of high-dimensional wavelet expansions[J]. J4, 2010, 45(10): 89-92.

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