Geodesic
Recovery of band-limited functions on locally compact Abelian groups from irregular samples
Czechoslovak Mathematical Journal, Tome 53 (2003) no. 2, pp. 249-264

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Using the techniques of approximation and factorization of convolution operators we study the problem of irregular sampling of band-limited functions on a locally compact Abelian group $G$. The results of this paper relate to earlier work by Feichtinger and Gröchenig in a similar way as Kluvánek’s work published in 1969 relates to the classical Shannon Sampling Theorem. Generally speaking we claim that reconstruction is possible as long as there is sufficient high sampling density. Moreover, the iterative reconstruction algorithms apply simultaneously to families of Banach spaces.
Classification : 22B99, 42C15, 43A15, 43A25, 47B38, 62D05, 94A12, 94A20
Keywords: irregular sampling; band-limited functions; locally compact Abelian group; solid Banach spaces 
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     author = {Feichtinger, H. G. and Pandey, S. S.},
     title = {Recovery of band-limited functions on locally compact {Abelian} groups from irregular samples},
     journal = {Czechoslovak Mathematical Journal},
     pages = {249--264},
     publisher = {mathdoc},
     volume = {53},
     number = {2},
     year = {2003},
     mrnumber = {1983449},
     zbl = {1021.43001},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2003__53_2_a2/}
}
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Feichtinger, H. G.; Pandey, S. S. Recovery of band-limited functions on locally compact Abelian groups from irregular samples. Czechoslovak Mathematical Journal, Tome 53 (2003) no. 2, pp. 249-264. http://geodesic.mathdoc.fr/item/CMJ_2003__53_2_a2/