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

IMAS (CONICET) - University of Buenos Aires, Argentina   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

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.

Joint work with Davide Barbieri (Universidad Autónoma de Madrid, Spain) and Eugenio Hernández (Universidad Autónoma de Madrid, Spain).

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