Pair Frames

TL;DR

This paper introduces the concept of pair frames, a generalization of traditional frames in frame theory, exploring their properties and new subclasses like (p, q)-pair frames and near identity pair frames.

Contribution

It presents the novel concept of pair frames and investigates their properties, expanding the framework of frame theory with new classes.

Findings

Pair frames generalize ordinary frames.

Introduction of (p, q)-pair frames.

Development of near identity pair frames.

Abstract

In this paper a new concept related to the frame theory is introduced; the notion of pair frame. By investigating some properties of such frames, it is shown that pair frames are a generalization of ordinary frames. Some classes of of them are introduced such as (p, q)-pair frames and near identity pair frames.