Robustness of infinite frames and Besselian structures

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.