Geodesic
Group reconstruction systems
The electronic journal of linear algebra, Tome 22 (2011), pp. 875-911.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: We consider classes of reconstruction systems (RS's) for finite dimensional real or complex Hilbert spaces H, called group reconstruction systems (GRS's), that are associated with representations of finite groups G. These GRS's generalize frames with high degree of symmetry, such as harmonic or geometrically uniform ones. Their canonical dual and canonical Parseval are shown to be GRS's. We establish simple conditions for one-erasure robustness. Projective GRS's, that can be viewed as fusion frames, are also considered. We characterize the Gram matrix of a GRS in terms of block group matrices. Unitary equivalences and unitary symmetries of RS's are studied. The relation between the irreducibility of the representation and the tightness of the GRS is established. Taking into account these results, we consider the construction of Parseval, projective and one-erasure robust GRS's.
Classification : 42C15, 42C40, 20C15, 05B20, 15A60
Keywords: reconstruction systems, fusion frames, g-frames, group representation, robustness, gram matrix 
@article{ELA_2011__22__a18,
     author = {Morillas, Patricia Mariela},
     title = {Group reconstruction systems},
     journal = {The electronic journal of linear algebra},
     pages = {875--911},
     publisher = {mathdoc},
     volume = {22},
     year = {2011},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ELA_2011__22__a18/}
}
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Morillas, Patricia Mariela. Group reconstruction systems. The electronic journal of linear algebra, Tome 22 (2011), pp. 875-911. http://geodesic.mathdoc.fr/item/ELA_2011__22__a18/