The present study deals with the recently introduced concept of P-woven frames. Two frames \(\left\{ \varphi _{i}\right\} _{i\in I}\) and \(\left\{ \psi _{i}\right\} _{i\in I}\) for a Hilbert space H are called P-woven, if there exists a nontrivial subset \(\sigma \) of I such that the family \(\left\{ g_{i}\right\} _{i\in I}\) represented as the triple \(\left( \left\{ \varphi _{i}\right\} ,\left\{ \psi _{i}\right\} ,\sigma \right) \) is a frame defined by \(g_i= \varphi _{i}\) if \(i\in \sigma \) and \(g_i=\psi _{i}\), otherwise. The duals of frames have an essential role in the reconstruction of vectors (or signals) in terms of the frame elements. In this paper we will prove some results in regards to P-woven property of the duals of P-woven frames. We then introduce the concept of P-woven duals of a collection of frames and obtain some necessary and sufficient conditions in which a collection of frames have P-woven duals.

本研究涉及最近引入的P编织框架的概念。两帧\（\ left \ {\ varphi _ {i} \ right \} _ {i \ in I} \）和\（\ left \ {\ psi _ {i} \ right \} _ {i \ in I } \）为Hilbert空间ħ被称为P-编织，如果存在一个非平凡子集\（\西格玛\）的我使得家庭\（\左\ {G_ {I} \右\} _ {I \在I} \中表示为三元组\（\ left（\ left \ {\ varphi _ {i} \ right \}，\ left \ {\ psi _ {i} \ right \}，\ sigma \ right）\ ）是由\（g_i = \ varphi _ {i} \）定义的框架，如果\（i \ in \ sigma \）和\（g_i = \ psi _ {i} \）， 除此以外。就帧元素而言，帧的对偶在向量（或信号）的重构中起着至关重要的作用。在本文中，我们将证明有关P编织框架对偶的P编织特性的一些结果。然后，我们介绍框架集合的P编织对偶的概念，并获得一些必要的充分条件，其中框架集合具有P编织的对偶。