On spectrally optimal duals for r-erasures of frames generated by graphs
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866913962064347136 |
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| author | Deepshikha Samanta, Aniruddha |
| author_facet | Deepshikha Samanta, Aniruddha |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_20347 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On spectrally optimal duals for r-erasures of frames generated by graphs Deepshikha Samanta, Aniruddha Functional Analysis 05C40, 05C50, 42C15, 42C40, 46C05 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. |
| title | On spectrally optimal duals for r-erasures of frames generated by graphs |
| topic | Functional Analysis 05C40, 05C50, 42C15, 42C40, 46C05 |
| url | https://arxiv.org/abs/2507.20347 |