Group reconstruction systems

MORILLAS PATRICIA MARIELA

ELECTRONIC JOURNAL OF LINEAR ALGEBRA

INT LINEAR ALGEBRA SOC

Lugar: Haifa; Año: 2011 vol. 22 p. 875 - 911

1081-3810

We consider classes of reconstruction systems (RS´s) for finitedimensional real or complex Hilbert spaces $mathcal{H}$, calledgroup reconstruction systems (GRS´s), that are associated withrepresentations of finite groups $mathcal{G}$. These GRS´sgeneralize frames with high degree of symmetry, such as harmonic orgeometrically uniform ones. Their canonical dual and canonicalParseval are shown to be GRS´s. We establish simple conditions forone erasure robustness. Projective GRS´s, that can be viewed asfusion frames, are also considered. We characterize the Gram matrixof a GRS in terms of block group matrices. Unitary equivalences andunitary symmetries of RS´s are studied. The relation between theirreducibility of the representation and the tightness of the GRS isestablished. Taking into account these results, we consider theconstruction of Parseval, projective and one erasure robust GRS´s.