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拟半双正交分数阶多小波框架的刻画

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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.
Description of quasi-semi-biorthogonal fractional multiwavelet frame
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.

wavelet frameframework theorymulti-resolution analysisfractional wavelet framequasi-semi-biorthogonal

刘瑞龙、陈清江

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西安建筑科技大学理学院,陕西西安 710055

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

国家自然科学基金陕西省自然科学基金

619023042021JQ-495

2024

纯粹数学与应用数学
西北大学

纯粹数学与应用数学

影响因子:0.233
ISSN:1008-5513
年,卷(期):2024.40(2)
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