Characterizations of woven frames

Animesh Bhandari; Saikat Mukherjee

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arXiv · 1809.09465

Characterizations of woven frames

Animesh Bhandari·Saikat Mukherjee

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Abstract

In a separable Hilbert space $\mathcal H$, two frames $\{f_i\}_{i \in I}$ and $\{g_i\}_{i \in I}$ are said to be woven if there are constants $0<A \leq B$ so that for every $\sigma \subset I$, $\{f_i\}_{i \in \sigma} \cup \{g_i\}_{i \in \sigma ^c}$ forms a frame for $\mathcal H$ with the universal bounds $A, B$. This article provides methods of constructing woven frames. In particular, bounded linear operators are used to create woven frames from a given frame. Several examples are discussed to validate the results. Moreover, the notion of woven frame sequences is introduced and characterized.

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BibTeX RIS

Animesh Bhandari, Saikat Mukherjee. 2018-09-25. Characterizations of woven frames. https://arxiv.org/abs/1809.09465

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