Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8899666 | Journal of Mathematical Analysis and Applications | 2018 | 17 Pages |
Abstract
The purpose of this paper is to study frames for a Hilbert space H, having the form {TnÏ}n=0â for some ÏâH and an operator T:HâH. We characterize the frames that have such a representation for a bounded operator T, and discuss the properties of this operator. In particular, we prove that the image chain of T has finite length N in the overcomplete case; furthermore {TnÏ}n=0â has the very particular property that {TnÏ}n=0Nâ1âª{TnÏ}n=N+ââ is a frame for H for all ââN0. We also prove that frames of the form {TnÏ}n=0â are sensitive to the ordering of the elements and to norm-perturbations of the generator Ï and the operator T. On the other hand positive stability results are obtained by considering perturbations of the generator Ï belonging to an invariant subspace on which T is a contraction.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Ole Christensen, Marzieh Hasannasab, Ehsan Rashidi,