Redundancy of Fusion frames in Hilbert Spaces

TL;DR

This paper extends the concept of redundancy from frames to fusion frames in Hilbert spaces, analyzing their properties, relationships with dual frames, and providing illustrative examples.

Contribution

It introduces the notion of redundancy for fusion frames, explores its properties, and examines connections with dual frames and local frame redundancies.

Findings

Redundancy of fusion frames is characterized by minimum and maximum values of a redundancy function.

The relationship between frame redundancy and dual fusion frames is established.

Examples illustrate the theoretical concepts and properties discussed.

Abstract

Upon improving and extending the concept of redundancy of frames, we introduce the notion of redundancy of fusion frames, which is concerned with the properties of lower and upper redundancies. These properties are achieved by considering the minimum and maximum values of the redundancy function which is defined from the unit sphere of the Hilbert space into the positive real numbers. In addition, we study the relationship between redundancy of frames (fusion frames) and dual frames (dual fusion frames). Moreover, we indicate some results about excess of fusion frames. We state the relationship between redundancy of local frames and fusion frames in a particular case. Furthermore, some examples are also given.