Quantitative bounds for unconditional pairs of frames
Functional Analysis
2022-12-05 v1 Numerical Analysis
Numerical Analysis
Abstract
We formulate a quantitative finite-dimensional conjecture about frame multipliers and prove that it is equivalent to Conjecture 1 in [SB2]. We then present solutions to the conjecture for certain classes of frame multipliers. In particular, we prove that there is a universal constant so that for all and the following is true. Let and be sequences in a finite dimensional Hilbert space which satisfy for all and If the frame operator for has eigenvalues and then has Bessel bound . The same holds for .
Keywords
Cite
@article{arxiv.2212.00947,
title = {Quantitative bounds for unconditional pairs of frames},
author = {Peter Balazs and Daniel Freeman and Roxana Popescu and Michael Speckbacher},
journal= {arXiv preprint arXiv:2212.00947},
year = {2022}
}
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19 pages