2025/07/27 by Deepshikha, Samanta, Aniruddha
#05C40 #05C50 #42C15 #42C40 #46C05 #FOS: Mathematics #Functional Analysis (math.FA)
paper · doi:10.48550/arxiv.2507.20347
In [9], authors studied spectrally optimal dual frames for 1-erasure and 2-erasures of frames generated by graph. In this paper, we study spectrally optimal dual frames for r-erasures. We show that the spectral radius of the error operator of unitary equivalent frames is same with respect to their respective canonical dual frames. We prove that if a frame is generated by a connected graph, then its canonical dual frame is the unique spectrally optimal dual frame for r-erasures. Further, we show that the canonical dual of frames generated by disconnected graphs are non-unique spectrally optimal dual frames for r-erasures.