数学物理学报 ›› 2017, Vol. 37 ›› Issue (2): 228-238.

• 论文 • 上一篇    下一篇

Fusion框架系统的局部框架扰动的稳定性

王维, 朱玉灿   

  1. 福州大学数学与计算机科学学院 福州 350116
  • 收稿日期:2016-06-12 修回日期:2016-11-24 出版日期:2017-04-26 发布日期:2017-04-26
  • 通讯作者: 朱玉灿 E-mail:zhuyucan@fzu.edu.cn
  • 作者简介:王维,476299152@qq.com
  • 基金资助:
    福建省自然科学基金(2016J01014,2014J01007)和福建省教育厅科技项目(JA14041)

Stability of Fusion Frame Systems under Perturbation of the Local Frame Vectors

Wang Wei, Zhu Yucan   

  1. College of Mathematics and Computer Science, Fuzhou University, Fuzhou 350116
  • Received:2016-06-12 Revised:2016-11-24 Online:2017-04-26 Published:2017-04-26
  • Supported by:
    Supported by the Natural Science Foundation of Fujian Province (2016J01014, 2014J01007) and the Office Fund of Fujian Provincial Education (JA14041)

摘要: 该文在Hilbert空间中一般的框架序列扰动形式下,利用正交投影的性质和对偶框架的性质研究了原序列张成的闭子空间与扰动序列张成的闭子空间的关系,并探讨了局部框架的一般扰动对fusion框架系统稳定性的影响.这些结果推广和改进了由Casazza,Kutyniok和Li等得到的著名结果.

关键词: 框架序列, 扰动, 局部框架, fusion框架系统, 稳定性

Abstract: This paper studies the relation between the two subspaces spanned by a frame sequence and its general perturbed version in Hilbert spaces by using the properties of orthogonal projection and the properties of dual frames. This paper also studies the stability of fusion frame systems under general perturbation of the local frame vectors. Our results generalize and improve the remarkable results which had been obtained by Casazza, Kutyniok and Li.

Key words: Frame sequence, Perturbation, Local frame, Fusion frame systems, Stability

中图分类号: 

  • O171.1