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Classification of general sequences by frame-related operators

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Balazs, Peter [Austrian Academy of Sciences] Stoeva, Diana T. [University of Architecture, Civil Engineering and Geodesy, Sofia] Antoine, Jean-Pierre [UCL]

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.

Document type Article de périodique (Journal article) – Article de recherche
Access type Accès libre
Publication date 2011
Language Anglais
Journal information "Sampling Theory in Signal and Image Processing : an international journal" - Vol. 10, no. 1-2, p. 151-170 (2011)
Peer reviewed yes
Publisher Sampling Publishing ((United States) Potsdam)
issn 1530-6429
Publication status Publié
Affiliations UCL - SST/IRMP - Institut de recherche en mathématique et physique
Austrian Academy of Sciences - Acoustics Research Institute
University of Architecture, Civil Engineering and Geodesy, Sofia - Dept of Mathematics
Keywords Analysis operator ; Synthesis operator ; frame operator ; Gram matrix ; Bessel sequence ; Frame ; Riesz Basis ; Lower frame sequence ; Riesz-Fischer sequence
Links
Bibliographic reference Balazs, Peter ; Stoeva, Diana T. ; Antoine, Jean-Pierre. Classification of general sequences by frame-related operators. In: Sampling Theory in Signal and Image Processing : an international journal, Vol. 10, no. 1-2, p. 151-170 (2011)
Permanent URL http://hdl.handle.net/2078.1/75171