小波型编织框架及其对偶性  

Wavelet weaving frame and the duality

作　　者：曹壮利 张建平 吴旭 CAO Zhuangli;ZHANG Jianping;WU Xu(College of Mathematics and Computer Science,Yan’an University,Yan’an 716000,China)

机构地区：[1]延安大学数学与计算机科学学院,陕西延安716000

出　　处：《延安大学学报（自然科学版）》2024年第3期91-96,共6页Journal of Yan'an University：Natural Science Edition

基　　金：国家自然科学基金项目(11961072);陕西省自然科学基础研究计划项目(2020JM-547);延安大学研究生教育创新计划项目(YCX2024042)。

摘　　要：Hilbert空间中编织框架为框架的一种特殊推广。本文在Hilbert空间中将编织型框架与小波型框架相结合,并用小波型编织框架的性质研究其对偶性,提出了小波型编织框架与对偶小波型编织框架的概念。首先,给出两个小波型编织框架互为对偶的充要条件;其次,给出了小波型框架的对偶框架在一定条件下可以编织成编织框架;最后,借助框架的相关性质,讨论了对偶小波型编织框架在数列扰动下的稳定性。研究结果推广了Hilbert空间中关于小波型编织框架性质研究的已有结论。The weaving frame in Hilbert spaces is a special promotion of the frame.In this paper,the weaving frame and wavelet-type frame are combined in Hilbert spaces,and the duality of the weaving frame is studied by using the properties of the weaving frame.Firstly,the sufficient and necessary conditions for the dual of two wavelet weaving frame are given.Secondly,the dual frame of wavelet frame can be woven into weaving frame under certain conditions.Finally,with the reference to the relevant properties of frames,the stability of dual wavelet-type weaving frame under series perturbation is discussed.The results of the study extend the existing conclusions about the properties of wavelet-type braided frames in Hilbert space.

关 键 词：编织框架 小波型编织框架 对偶框架 扰动 

分 类 号：O174.2[理学—数学]