Characterizations of woven frames

TL;DR

This paper explores methods for constructing woven frames in Hilbert spaces, using bounded linear operators, and introduces the concept of woven frame sequences with characterizations and examples.

Contribution

It introduces new methods to construct woven frames via bounded linear operators and defines woven frame sequences with their properties.

Findings

Methods for constructing woven frames using bounded linear operators.

Introduction and characterization of woven frame sequences.

Validation of methods through several examples.

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.