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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
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[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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