Hilbert空间中K-Riesz框架的和

详细信息    查看全文 | 推荐本文 |

英文篇名：Sums of K-Riesz frames in Hilbert spaces 作者：黄新丽 ; 朱玉灿 英文作者：HUANG Xinli;ZHU Yucan;Liberal Arts College, Fuzhou Institute of Technology;College of Mathematics and Computer Science, Fuzhou University; 关键词：Riesz框架 ; K-框架 ; K-Riesz框架 ; 和 英文关键词：Riesz frame;;K-frame;;K-Riesz frame;;sum 中文刊名：FZDZ 英文刊名：Journal of Fuzhou University(Natural Science Edition) 机构：福州理工学院文理学院;福州大学数学与计算机科学学院; 出版日期：2019-05-20 16:23 出版单位：福州大学学报(自然科学版) 年：2019 期：v.47;No.229 基金：福建省自然科学基金资助项目(2016J01014);; 福建省中青年教师教育教学研究资助项目(JAT170803) 语种：中文; 页：FZDZ201903001 页数：5 CN：03 ISSN：35-1117/N 分类号：5-9

摘要

针对一个K-Riesz框架与一个序列的和如何能构成新K-Riesz框架的问题,提出用算子理论研究的方法,得到构成新K-Riesz框架的充分条件.所得结论更正Riesz框架中的相关结论.
        According to the operate theory, the paper suggest a new research method to solve the problem of how the sum of a K-Riesz frame and a sequence generating a new K-Riesz frame. Then the sufficient conditions for generating a new K-Riesz frame are obtained. The results in the paper correct the remarkable results of Riesz-frames.

引文

[1] DUFFIN R J,SCHAEFFER A C.A class of nonharmonic Fourier series[J].Transactions of the American Mathematical Society,1952,72(3):341-366.
    [2] HEATH R W J,PAULRAJ A J.Linear dispersion codes for MIMO systems based on frame theory[J].IEEE Transactions on Signal Processing,2002,50(10):2429-2441.
    [3] HAN D G,LYU F S,SUN W C.Recovery of signals from unordered partial frame coeffients[J].Applied and Computational Harmonic Analysis,2018,44(1):38-58.
    [4] CHRISTENSEN O.Frames containing a Riesz basis and approximation of the frame coefficients using finite-dimensional methods[J].Journal of Mathematical Analysis and Applications,1996,199(1):256-270.
    [5] G?VRUTA L.Frames for operators[J].Applied and Computational Harmonic Analysis,2012,32(1):139-144.
    [6] 黄永东,化定丽.Hilbert 空间中的K-Riesz框架及其稳定性[J].中国科学(数学),2017,47(3):383-396.
    [7] 郭燕妮,周家云.Riesz框架稳定性和摄动的研究[J].数学学报,2003,46(4):673-682.
    [8] RAMU G,JOHNSON P S.Frame operators of K-frames[J].Sema Journal,2016,73(2):171-181.
    [9] TAYLOR A E,LAY D C.Introduction to functional analysis[M].New York:Wiley,1980.
    [10] ASGARI M S,RAHIMI H.Generalized frames for operators in Hilbert spaces[J].Infinite Dimensional Analysis,Quantum Probability and Related Topics,2014,17(2):1450013(1-20).