2017/04/29 by Fahimeh Arabyani Neyshaburi, Neyshaburi, Fahimeh Arabyani, Ali Akbar Arefijamaal +1
Engineering · Mathematics · #42C15 #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Analysis and Transform Methods #Photoacoustic and Ultrasonic Imaging
paper · pdf · doi:10.48550/arxiv.1705.00209
openalex publication_date 2017/04/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
K-frames, a new generalization of frames, were recently considered by L.\nGavruta in connection with atomic systems and some problems arising in sampling\ntheory. Also, fusion frames are an important generalization of frames, applied\nin a variety of applications. In the present paper, we introduce the notion of\nK-fusion frames in Hilbert spaces and obtain several approaches for identifying\nof K-fusion frames. The main purpose is to reconstruct the elements from the\nrange of the bounded operator K on a Hilbert space H by using a family of\nclosed subspaces in H. This work will be useful in some problems in sampling\ntheory which are processed by fusion frames. For this end, we present some\ndescriptions for duality of K-fusion frames and also resolution of the operator\nK to provide simple and concrete constructions of duals of K-fusion frames.\nFinally, we survey the robustness of K-fusion frames under some perturbations.\n