Characterizations of woven frames

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 $0<A\le B$ 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.

19 pages