Effects of permutation functions on woven and non-woven frames. (English) Zbl 07841658
Two frames \(\{\varphi_i\}_{i\in I}\) and \(\{\psi_i\}_{i\in I}\) for a Hilbert space \(H\) are woven if for every subset \(\sigma\subset I,\) the family \(\{\varphi_i\}_{i\in \sigma} \cup \{\psi_i\}_{i\in\sigma^c}\) is a frame for \(H.\) The fundamental properties of woven frames were studied in [T. Bemrose et al., Oper. Matrices 10, No. 4, 1093–1116 (2016; Zbl 1358.42025)]. This article discusses how a permutation in the set of indices of one of the frames affects whether the two new frames are woven or not.
Reviewer: Antonio Galbis (València)
MSC:
| 42C15 | General harmonic expansions, frames |
| 42C40 | Nontrigonometric harmonic analysis involving wavelets and other special systems |
Citations:
Zbl 1358.42025References:
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