Compare and contrast between duals of fusion and discrete frames

TL;DR

This paper explores the complex structure of duals in fusion frames, comparing them with discrete frames, and clarifies their relationships, which are not straightforward as in the case of discrete frames.

Contribution

It provides a detailed analysis of the duals of fusion frames and their relation to associated discrete frames, addressing the complexity in their dual structures.

Findings

Duals of fusion frames have a complex structure unlike discrete frames.

The paper clarifies the relationship between fusion frame duals and discrete frame duals.

Fusion frames' duals are not always duals in the traditional sense, unlike discrete frames.

Abstract

Fusion frames are valuable generalizations of discrete frames. Most concepts of fusion frames are shared by discrete frames. However, the dual setting is so complicated. In particular, unlike discrete frames, two fusion frames are not dual of each other in general. In this paper, we investigate the structure of the duals of fusion frames and discuss the relation between the duals of fusion frames with their associated discrete frames.