## Contributed talks session B (Thursday)

#### Location

Cupples I Room 218

#### Start Date

7-21-2016 3:00 PM

#### End Date

21-7-2016 3:20 PM

#### Description

We consider systems of vectors of form $$\{A^nh_i:\;i\in I, n\geq 0$$ where $\{h_i\}_{i\in I}$ is a countable (finite or infinite) system of vectors in a separable Hilbert space $\mathcal{H}$ and $A\in B(\mathcal{H})$ 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 $$\{\pi(g) h_i:\;i\in I, g\in \Gamma \}$$ where $\pi$ is a unitary representation on $\mathcal{H}$ of a discrete group $\Gamma$ and extract information about the spectrum of the operators $\pi(g)$ when the system is minimal or complete and Bessel. The initial motivation for considering these problems comes from what is called dynamical sampling problem.

#### Share

COinS

Jul 21st, 3:00 PM Jul 21st, 3:20 PM

Frames and Bessel systems generated by the iterative actions of operators

Cupples I Room 218

We consider systems of vectors of form $$\{A^nh_i:\;i\in I, n\geq 0$$ where $\{h_i\}_{i\in I}$ is a countable (finite or infinite) system of vectors in a separable Hilbert space $\mathcal{H}$ and $A\in B(\mathcal{H})$ 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 $$\{\pi(g) h_i:\;i\in I, g\in \Gamma \}$$ where $\pi$ is a unitary representation on $\mathcal{H}$ of a discrete group $\Gamma$ and extract information about the spectrum of the operators $\pi(g)$ when the system is minimal or complete and Bessel. The initial motivation for considering these problems comes from what is called dynamical sampling problem.