AUTHOR=Aceska Roza , Kim Yeon H. 

TITLE=Scalability of Frames Generated by Dynamical Operators

JOURNAL=Frontiers in Applied Mathematics and Statistics

VOLUME=Volume 3 - 2017

YEAR=2017

URL=https://www.frontiersin.org/journals/applied-mathematics-and-statistics/articles/10.3389/fams.2017.00022

DOI=10.3389/fams.2017.00022

ISSN=2297-4687

ABSTRACT=Let H be  a separable    Hilbert space, let  G be a subset of H, and  let A be an operator on H.   Under appropriate conditions on A and G, it is known that the set  of iterations   F_G(A) 
is a  frame for H. We call  F_G(A)  a dynamical frame for H, and  explore further  its properties; in particular, we show  that its canonical dual frame also has an iterative set structure. 

 
We explore the relations between the operator A,  the set G and the number of iterations L which ensure that the system  F_G(A)  is a scalable frame. We give a general statement on frame scalability, and study in detail the   case   when A is a normal operator, utilizing the unitary diagonalization. In addition, we   answer the question of when F_G(A)  is a scalable frame in several special cases involving block-diagonal and companion operators.