# Multi-Window Weaving Frames

## TL;DR

This paper extends the concept of weaving frames to multi-window Gabor frames, providing new criteria for their woven property using phase space localization and examples with Hermite functions.

## Contribution

It introduces the first sufficient criteria for multi-window Gabor frames to be woven, including Hilbert space and phase space pointwise conditions.

## Key findings

- Established Hilbert space norm criterion for weaving
- Developed phase space pointwise criterion for weaving
- Provided examples with Hermite functions as woven frames

## Abstract

In this work we deal with the recently introduced concept of weaving frames. We extend the concept to include multi-window frames and present the first sufficient criteria for a family of multi-window Gabor frames to be woven. We give a Hilbert space norm criterion and a pointwise criterion in phase space. The key ingredient are localization operators in phase space and we give examples of woven multi-window Gabor frames consisting of Hermite functions.