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《山东大学学报(理学版)》 ›› 2024, Vol. 59 ›› Issue (4): 73-80.doi: 10.6040/j.issn.1671-9352.0.2022.468

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连续广义框架的ε-近似

张伟()   

  1. 河南财经政法大学数学与信息科学学院, 河南 郑州 450046
  • 收稿日期:2022-09-07 出版日期:2024-04-20 发布日期:2024-04-12
  • 作者简介:张伟(1979—), 男, 副教授, 博士, 研究方向为小波分析及其应用. E-mail: zwfylhappy@126.com
  • 基金资助:
    河南省高等学校重点科研项目(21A110004);河南省科技攻关项目(242102210049)

ε-approximations of continuous generalized frames

Wei ZHANG()   

  1. School of Mathematics and Information Sciences, Henan University of Economics and Law, Zhengzhou 450046, Henan, China
  • Received:2022-09-07 Online:2024-04-20 Published:2024-04-12

摘要:

讨论Hilbert空间中连续广义框架理论, 引入了连续广义框架的ε-近似、ε-接近的概念, 建立二者之间的联系, 得到一定条件下连续广义框架ε-近似也是连续广义框架, 但有趣的是, 紧连续广义框架ε-近似不可能是紧连续广义框架; 给定一个连续广义框架的对偶框架及ε-接近, 可以找到其ε-接近的一个对偶连续广义框架使得两个对偶框架彼此靠近。

关键词: 连续广义框架, 连续广义对偶框架, ε-近似

Abstract:

This paper addresses the continuous generalized frame theory in Hilbert spaces. We introduce the concepts of ε-approximation, ε-closeness of continuous generalized frames, and establish a link between ε-approximation and ε-closeness. We present that the ε-approximations of continuous generalized frames are continuous generalized frames under certain conditions. Interestingly, the ε-approximations of tight continuous generalized frames can not be tight continuous generalized frames. Given a dual frame and ε-closeness of a continuous generalized frame, one can find a dual continuous generalized frame of its ε-closeness that makes the two dual continuous generalized frames close to each other.

Key words: continuous generalized frames, dual continuous generalized frames, ε-approximation

中图分类号: 

  • O174.2
1 DUFFINR J,SCHAEFFERA C.A class of nonharmonic Fourier series[J].Transactions of the American Mathematical Society,1952,72(2):341-366.
doi: 10.1090/S0002-9947-1952-0047179-6
2 DAUBECHIESI,GROSSMANNA,MEYERY.Painless nonorthogonal expansions[J].Journal of Mathematical Physics,1986,27(5):1271-1283.
doi: 10.1063/1.527388
3 CHRISTENSENO.An introduction to frames and Riesz bases[M].Boston:Birkhäuser,2016.
4 CHRISTENSENO,HASANNASABM.Frame properties of systems arising via iterated actions of operators[J].Applied and Computational Harmonic Analysis,2019,46(3):664-673.
doi: 10.1016/j.acha.2018.04.002
5 ABDOLLAHPOURM R,KHEDMATIY.On some properties of continuous g-frames and Riesz-type continuous g-frames[J].Indian Journal of Pure and Applied Mathematics,2017,48(1):59-74.
doi: 10.1007/s13226-016-0208-1
6 肖祥春,曾晓明.连续g-框架的刻画[J].数学学报,2012,55(6):1131-1144.
XIAOXiangchun,ZENGXiaoming.Characterizations of continuous g-frames[J].Acta Mathematica Sinica,2012,55(6):1131-1144.
7 ALIS T.Continuous frames in Hilbert space[J].Annals of Physics,1993,222(1):1-37.
8 SUNW C.G-frames and g-riesz bases[J].Journal of Mathematical Analysis and Applications,2006,322(1):437-452.
doi: 10.1016/j.jmaa.2005.09.039
9 ABDOLLAHPOURM R,FAROUGHIM H.Continuous G-frames in Hilbert spaces[J].Southeast Asian Bull Math,2008,32(1):1-19.
10 CHRISTENSENO,HASANNASABM.Approximate frame representations via iterated operator systems[J].Studia Mathematica,2022,263(1):1-18.
doi: 10.4064/sm190228-5-8
11 CHRISTENSENO,HASANNASABM,STEIDLG.On approximate operator representations of sequences in Banach spaces[J].Complex Analysis and Operator Theory,2021,15(3):1-22.
12 XIAOX C,ZENGX M.Some equalities and inequalities of g-continuous frames[J].Science China Mathematics,2010,53(10):2621-2632.
[1] 张伟,付艳玲. Hilbert空间中连续广义框架的分解[J]. 《山东大学学报(理学版)》, 2019, 54(8): 76-80.
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