Robustness of infinite frames and Besselian structures

TL;DR

This paper investigates the robustness and minimal redundancy conditions of infinite frames and Besselian structures in Hilbert spaces, providing new theoretical insights into their stability under erasures.

Contribution

It introduces a comprehensive framework for MRC and robustness of erasures for infinite frames, exploring their relationships and implications for Besselian frames.

Findings

Established a framework linking MRC and robustness in infinite frames

Analyzed the interplay between robustness, MRC, and frame excess

Provided insights into erasure resilience of Besselian frames

Abstract

This paper extends the concepts of Minimal Redundancy Condition (MRC) and robustness of erasures for infinite frames in Hilbert spaces. We begin by establishing a comprehensive framework for the MRC, emphasizing its importance in ensuring the stability and resilience of frames under finite erasures. Furthermore, we discussed the robustness of erasures, which generalizes the ability of a frame to withstand information loss. The relationship between robustness, MRC, and excess of a frame is carefully examined, providing new insights into the interplay between these properties. The robustness of Besselian frames, highlighting their potential in applications where erasure resilience is critical. Our results contribute to a deeper understanding of frame theory and its role in addressing challenges posed by erasure recovery.