Frames and Bessel systems generated by the iterative actions of operators

We consider systems of vectors of the form {Ahi : i ∈ I, n ≥ 0} where {hi}i∈I is a countable (finite or infinite) system of vectors in a separable Hilbert space H and A ∈ B(H) is a bounded operator. We show that a system of that form can never be both complete and minimal, and find conditions that the operator A needs to satisfy for the system to be a frame or a complete Bessel system. We also investigate systems of form {π(g)hi : i ∈ I, g ∈ Γ} where π is a unitary representation on H of a discrete group Γ and extract information about the spectrum of the operators π(g) when the system is minimal or complete and Bessel. The initial motivation for considering these problems comes from what is called dynamical sampling problem. Talk time: 2016-07-21 03:00 PM— 2016-07-21 03:20 PM Talk location: Cupples I Room 218