## View abstract

### Session S13 - Harmonic Analysis, Fractal Geometry, and Applications

Friday, July 16, 13:45 ~ 14:15 UTC-3

## Frames generated by the action of a discrete group

### Victoria Paternostro

In this talk we shall discuss the structure of subspaces of a Hilbert space that are invariant under unitary representations of discrete groups. We will study in depth the reproducing properties (this is, being a Riesz basis or a frame) of countable families of orbits. In particular we shall see that every separable Hilbert space $\mathcal{H}$ for which there exists a dual integrable representation $\Pi$ of a discrete group $\Gamma$ on $\mathcal{H}$, admits a Parseval frame of the form $\{\Pi(\gamma)\phi:\,\gamma\in\Gamma, \phi\in\Phi\}$ where $\Phi\subseteq \mathcal{H}$ is an at most countable set. Our results extend those that already exist in the euclidean case to this more general context.