Fusion框架系统的局部框架扰动的稳定性

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

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.

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 orthogo- nal 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 bv Casazza. Kutvniok and Li.