Fibers as a tool to characterize frames of translates

PATERNOSTRO VICTORIA

Marseille

Seminario; Seminar of Signal Processing-Machne Learning; 2014

In this talk we will see how to analyze frame properties on systems of translatesusing fiberization techniques. We will first discuss the concept of fibers in $L^2(R^d)$ and its relationship with systems of the form ${T_kp: kinZ, pin A}$ where $A$ is a set of functions in  $L^2(R^d)$ and $T_k$ is the shift operator by $k$. We will then seehow this notion can be defined in more general contexts than $L^2(R^d)$. Mainly, wewill work with fibers designed to deal with systems in Hilbert spaces generated bythe action of a discrete group. We will provide several examples to illustrate thetheory. The results we present in this talk are in collaboration with D. Barbieri, C. Cabrelli and E. Hernandez.