Geodesic
Representation of Parseval frames in Hilbert spaces
Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, no. 5 (2011), pp. 60-70

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In this paper we introduce two new classes of Parseval frames in arbitrary Hilbert spaces of finite or infinite dimension: simple and composite Parseval frames. Theorems of representation of composite Parseval frames by summation of simple ones are proved. Few classes of simple frames are described: orthonormal basis, equiangular Parseval frames and some other examples.
Keywords: Parseval frames, frame equivalence, frame representations, equiangular frames. 
@article{VSGU_2011_5_a6,
     author = {I. S. Ryabtsov},
     title = {Representation of {Parseval} frames in {Hilbert} spaces},
     journal = {Vestnik Samarskogo universiteta. Estestvennonau\v{c}na\^a seri\^a},
     pages = {60--70},
     publisher = {mathdoc},
     number = {5},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VSGU_2011_5_a6/}
}
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I. S. Ryabtsov. Representation of Parseval frames in Hilbert spaces. Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, no. 5 (2011), pp. 60-70. http://geodesic.mathdoc.fr/item/VSGU_2011_5_a6/