Studying Perturbations of K-Frames

In this paper, we explore the concept of K-frames, which are fundamentalstructures in frame theory widely used in signal processing and image reconstruction. Webegin by discussing equivalent characterizations for K-frames, highlighting their connec-tions to atomic systems and Bessel sequences. We then introduce the notion of K-dualframes and define perturbations of K-frames.Our main result is a theorem characterizing perturbations of K-frames. We establishconditions under which a perturbed K-frame remains a K-frame, providing bounds forthe perturbed frame and demonstrating its stability.This paper contributes to a deeper understanding of the stability and robustness ofK-frames under perturbations, offering valuable insights for their application in variousfields, including signal processing and image reconstruction.

کلیدواژه ها:

K-frames ، K-duals ، perturbation.