Mathematics – Classical Analysis and ODEs
Scientific paper
2005-05-09
Mathematics
Classical Analysis and ODEs
20 pages, to appear in "The Journal of Sampling Theory in Signal and Image Processing", typos corrected
Scientific paper
Sampling theory in spaces other than the space of band-limited functions has recently received considerable attention. This is in part because the band-limitedness assumption is not very realistic in many applications. In addition, band-limited functions have very slow decay which translates in poor reconstruction. In this article we study the sampling problem in general shift invariant spaces. We characterize the functions in these spaces and provide necessary and sufficient conditions for a function in $L^2(\R)$ to belong to a sampling space. Furthermore we obtain decompositions of a sampling space in sampling subspaces. These decompositions are related with determining sets. Some examples are provided.
Blanco Cristina
Cabrelli Carlos
Heineken Sigrid
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