Classification of General Sequences by Frame-Related Operators

Details Classification of General Sequences by Frame-Related Operators Classification of General Sequences by Frame-Related Operators

2010-09-08

arxiv.org/abs/1009.1496v1

Mathematics

Functional Analysis

Scientific paper

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.

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