2010/09/08 by Peter Balazs, Diana T. Stoeva, Jean-Pierre Antoine · 1 citation
Mathematics · #math.FA
published as Sampling Theory in Signal and Image Processing (STSIP) Vol. 10 (1-2), pp. 151-170 (2011)
arxiv created 2010/09/08 · arxiv updated 2012/05/31
This note is a survey and collection of results, as well as presenting some original research. For Bessel sequences and frames, the analysis, synthesis and frame operators as well as the Gram matrix are well-known, bounded operators. We investigate these operators for arbitrary sequences, which in general lead to possibly unbounded operators. We characterize various classes of sequences in terms of these operators and vice-versa. Finally, we classify these sequences by operators applied on orthonormal bases.