拟半双正交分数阶多小波框架的刻画
Description of quasi-semi-biorthogonal fractional multiwavelet frame
刘瑞龙 1陈清江1
作者信息
- 1. 西安建筑科技大学理学院,陕西西安 710055
- 折叠
摘要
本文在半正交分数阶多小波框架的基础上,运用多分辨分析,泛函分析,矩阵理论研究L2(R)上多元小波框架的特征,将半正交分数阶多小波框架推广到拟半双正交分数阶多小波框架,给出了拟半双正交分数阶多小波框架的概念,得到了严格拟半双正交分数阶多小波框架的等价条件,证明了广义多分辨分析分数阶规范对偶多小波框架与拟半双正交分数阶规范对偶多小波框架满足等价条件.
Abstract
Based on the semi-orthogonal fractional multiwavelet frames and using multi-resolution analysis,functional analysis and matrix theory are used to study the characteristics of the mul-tivariate wavelet framework on L2(R).The semi-orthogonal fractional multiwavelet frames are generalized to the quasi-semi-biorthogonal fractional multiwavelet framework,equivalence condi-tions for a strictly quasi-biorthogonal fractional multiwavelet frames are obtained.Prove that the generalized multiresolution analytical fractional gauge dual multiwavelet framework and the quasi-biorthogonal fractional gauge dual multiwavelet framework satisfy the equivalence relation.
关键词
小波框架/框架理论/多分辨分析/分数阶小波框架/拟半双正交Key words
wavelet frame/framework theory/multi-resolution analysis/fractional wavelet frame/quasi-semi-biorthogonal引用本文复制引用
基金项目
国家自然科学基金(61902304)
陕西省自然科学基金(2021JQ-495)
出版年
2024
NETL
NSTL
万方数据