24 August 2015 The unconditional constants of frame expansions and cross-frame expansions
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Abstract
It was shown in Ref. 1 that the unconditional constant for frame expansions is √B/A, where A and B are the frame bounds of the frame. It was also shown that a Bessel sequence is 1-unconditional if and only if it can be partitioned into an orthogonal sum of tight frames. In Ref. 2 cross-frame expansions were considered. It was shown that as long as the cross-frame expansions stay uniformly bounded away from zero, then similar results could be obtained. In this paper, we summarize these results into one concise source as well as add a few basic results that were not considered before.
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Travis Bemrose, Travis Bemrose, Peter G. Casazza, Peter G. Casazza, Richard G. Lynch, Richard G. Lynch, } "The unconditional constants of frame expansions and cross-frame expansions", Proc. SPIE 9597, Wavelets and Sparsity XVI, 959716 (24 August 2015); doi: 10.1117/12.2186900; https://doi.org/10.1117/12.2186900
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