多分辨分析的相似性  

Similarity for multiresolution analyses

作　　者：李忠艳[1] LI Zhongyan(School of Mathematics and Physics,North China Electric Power University,102206,Beijing,PRC)

机构地区：[1]华北电力大学数理学院,北京市102206

出　　处：《曲阜师范大学学报（自然科学版）》2022年第3期83-88,共6页Journal of Qufu Normal University(Natural Science)

基　　金：国家自然科学基金(11571107).

摘　　要：正交多分辨分析M={V_(n),n∈Z}是Hilbert空间H=L^(2)(ℝ)中满足一系列条件闭子空间的套.该文从套代数理论的角度考察所有正交多分辨分析构成的集合.基于多分辨分析可以用局部换位算子参数化的事实以及Larson(1979)和Dai(1990)关于套代数的刻画理论,说明了H中任意两个多分辨分析都是相似的和算子代数B(H)是任意多分辨分析生成套代数双模的结论.An orthogonal multiresolution analysis M={V_(n),n∈Z}is a nest that is a set of closed subspaces with a series of conditions in the Hilbert space H=L^(2)(ℝ).The set of all orthogonal multiresolution analyses from the perspective of the theory of nest algebras is investigated.Based on the fact that multiresolution analyses can be parameterized by local commutant operators and the characterizations of nest algebras by Larson(1979)and Dai(1990),it is obtained that any two multiresolution analyses H are similar and the operator algebra B(H)is the bimodules of nest algebra generated by any multiresolution analysis.

关 键 词：多分辨分析 套 套代数 

分 类 号：O177[理学—数学]