CONICET | Buscador de Institutos y Recursos Humanos

This paper considers group reconstruction systems (GRS´s), for finite dimensional real or complex Hilbert spaces $mathcal{H}$, that are associated with unitary representations of finite abelian groups. The relation between these GRS´s and the generalized Fourier matrix is established. A special type of Parseval GRS, called harmonic reconstruction system (HRS), is defined. We show that there exist HRS´s that present maximal robustness to erasures given characterizations of certain families.