2021
DOI: 10.48550/arxiv.2106.00511
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Completion versus removal of redundancy by perturbation

Abstract: A sequence {g k } ∞ k=1 in a Hilbert space H has the expansion prop-In this paper we analyze the question whether there exist small norm-perturbations of {g k } ∞ k=1 which allow to represent all f ∈ H; the answer turns out to be yes for frame sequences and Riesz sequences, but no for general basic sequences. The insight gained from the analysis is used to address a somewhat dual question, namely, whether it is possible to remove redundancy from a sequence with the expansion property via small norm-perturbatio… Show more

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