Discretization of Continuous Frame

Proceedings Mathematical Sciences

A Fattahi¹  H Javanshiri² 

[1] Department of Mathematics, Razi University, Kermanshah, Iran$$;Department of Mathematical Sciences, Isfahan University of Technology, Isfahan -, Iran$$

关键词: Bounded operator;    Hilbert space;    continuous frame;    atomic resolution of identity.;   

DOI  :  

学科分类：数学（综合）

来源: Indian Academy of Sciences

【 摘 要 】

In this paper we consider the notion of continuous frame of subspaces and define a new concept of continuous frame, entitled continuous atomic resolution of identity, for arbitrary Hilbert space $mathcal{H}$ which has a countable reconstruction formula. Among the other results, we characterize the relationship between this new concept and other known continuous frames. Finally, we state and prove the assertions of the stability of perturbation in this concept.

【 授权许可】

Unknown