拟半双正交分数阶多小波框架的刻画  

Description of quasi-semi-biorthogonal fractional multiwavelet frame

作　　者：刘瑞龙 陈清江[1] LIU Ruiong;CHEN Qingjiang(School of Science,Xi′an University of Architectural Science and Technology,Xi′an 710055,China)

机构地区：[1]西安建筑科技大学理学院,陕西西安710055

出　　处：《纯粹数学与应用数学》2024年第2期327-338,共12页Pure and Applied Mathematics

基　　金：国家自然科学基金(61902304);陕西省自然科学基金(2021JQ-495)。

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L~2(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.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 multivariate wavelet framework on L~2(R). The semi-orthogonal fractional multiwavelet frames are generalized to the quasi-semi-biorthogonal fractional multiwavelet framework, equivalence conditions for a strictly quasi-biorthogonal fractional multiwavelet frames are obtained. Prove that the generalized multiresolution analytical fractional gauge dual multiwavelet framework and the quasibiorthogonal 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 

分 类 号：O174.2[理学—数学]