Classification of general sequences by frame-related operators
(2011) Sampling Theory in Signal and Image Processing : an international journal — Vol. 10, n° 1-2, p. 151-170 (2011)
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- Authors
Antoine, Jean-Pierre 
- Abstract
- 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.
- Affiliations
Austrian Academy of Sciences Acoustics Research Institute University of Architecture, Civil Engineering and Geodesy, Sofia Dept of Mathematics
Citations
Balazs, P., Stoeva, D. T., & Antoine, J.-P. (2011). Classification of general sequences by frame-related operators. Sampling Theory in Signal and Image Processing : an international journal, 10(1-2), 151-170. https://hdl.handle.net/2078.5/24868 (Original work published 2011)