Hilbert空间上的加权测度框架  

WEIGHTED MEASURE FRAMES ON HILBERT SPACES

作　　者：张超华 李鹏同[1] Zhang Chaohua;Li Pengtong(College of Science,Nanjing University of Aeronautics and Astronautics,Nanjing 210016)

机构地区：[1]南京航空航天大学理学院,南京210016

出　　处：《南京大学学报（数学半年刊）》2018年第1期54-69,共16页Journal of Nanjing University(Mathematical Biquarterly)

基　　金：国家自然科学基金(No.11671201)

摘　　要：文推广了Hilbert空间上的离散框架,引入并研究了Hilbert空间上的加权测度框架.刻画了Bessel加权测度、Parseval加权测度框架的性质,给出了加权测度框架的判定条件.此外,我们引入伪对偶及近似对偶的概念,研究了加权测度框架的近似对偶问题.最后给出了有限维Hilbert空间上加权测度框架的相关性质.As a generalization of discrete frames for Hilbert spaces,we introduce the notion of weighted measure frames on Hilbert spaces and give its judging criteria.The properties of Bessel weighted mea-sure,Parseval weighted measure frames are also investigated by using operator theory.We introduce the definition of approximately-dual and pseudo-dual of Bessel weighted measure,and construct approxi-mately dual frames via perturbation theory.Finally some results about the weighted measure frames in finite dimensional Hilbert spaces are obtained.

关 键 词：加权测度框架 框架算子 分析算子 正交性 对偶性 

分 类 号：O177.1[理学—数学]