Codes and Expansions (CodEx) Seminar

Victor Bailey (Georgia Tech)
Frames via Unilateral Iterations of Bounded Operators

Dynamical Sampling is, in a sense, a hypernym classifying the set of inverse problems arising from considering samples of a signal and its future states under the action of a bounded linear operator. Recent works in this area consider questions such as when can a given frame for a separable Hilbert Space, \(\{f_k\}_{k \in I} \subset H\), be represented by iterations of an operator on a single vector and what are necessary and sufficient conditions for a system, \(\{T^n \varphi\}_{n=0}^{\infty} \subset H\), to be a frame? In this talk, we will discuss the connection between frames given by iterations of a bounded operator and the theory of model spaces in the Hardy-Hilbert Space as well as necessary and sufficient conditions for a system generated by the orbit of a pair of commuting bounded operators to be a frame.