小波框架的某些判定准则

郭训香

数学学报 ›› 2011, Vol. 54 ›› Issue (1) : 159-168.

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PDF(493 KB)
数学学报 ›› 2011, Vol. 54 ›› Issue (1) : 159-168. DOI: 10.12386/A2011sxxb0017
论文

小波框架的某些判定准则

    郭训香
作者信息 +

Some Criterions on Wavelet Frames

    Xun Xiang GUO
Author information +
文章历史 +

摘要

本文首先给出了希尔伯特空间H上两个半小波框架序列成为小波框架的一个充分条件,该结论与框架的扰动理论有关.然后建立了通过膨胀与平移母函数生成L2(R)上的小波框架的膨胀参数,平移参数以及母函数的一些充分条件. 这些结果推广了小波框架理论中经典文献中的相关结论.我们还对贝塞尔序列进行了讨论, 并得到了一些有趣的结论.

 

Abstract

In this paper, firstly we give a condition for two semi-frame sequences such that both of them be frames for Hilbert space H, which is related to the perturbation theory of frames. Then we give some conditions on dilation and translation parameters and the generating functions such that wavelet frames for L2(R) are generated. These results generalize the classical similar results in literatures. We also discuss the Bessel sequence and add some other sufficient conditions.

 

关键词

框架 / 标准正交基 / 贝塞尔序列

Key words

frame / orthonormal basis / Bessel sequence

引用本文

导出引用
郭训香. 小波框架的某些判定准则. 数学学报, 2011, 54(1): 159-168 https://doi.org/10.12386/A2011sxxb0017
Xun Xiang GUO. Some Criterions on Wavelet Frames. Acta Mathematica Sinica, Chinese Series, 2011, 54(1): 159-168 https://doi.org/10.12386/A2011sxxb0017

参考文献


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基金

教育部留学归国基金项目SRF([2008]890);江西省自然科学基金资助项目(2008GZS0024);西南财经大学第三期211青年成长项目

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