On spectrally optimal duals for r-erasures of frames generated by graphs
Functional Analysis
2025-07-29 v1
Abstract
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.
Cite
@article{arxiv.2507.20347,
title = {On spectrally optimal duals for r-erasures of frames generated by graphs},
author = {Deepshikha and Aniruddha Samanta},
journal= {arXiv preprint arXiv:2507.20347},
year = {2025}
}
Comments
18 pages. arXiv admin note: substantial text overlap with arXiv:2406.00776