Optimal K dual frames and pairs in the presence of erasures
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866908477689954304 |
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| author | Mondal, Shankhadeep Han, Deguang Mohapatra, R. N. |
| author_facet | Mondal, Shankhadeep Han, Deguang Mohapatra, R. N. |
| contents | This paper explores the structure of optimal K-dual frames for a given K-frame and optimal K-dual pairs, within the context of erasures which occur during the transmission of frame coefficients. We address two distinct erasure scenarios and examine their impact on the reconstruction process. The optimality criteria are defined in terms of minimizing the spectral radius and the operator norm of the associated error operators. Through this approach, we provide a comprehensive framework for understanding and mitigating the effects of erasures in frame theory, contributing to enhanced robustness in data transmission and recovery. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_01964 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Optimal K dual frames and pairs in the presence of erasures Mondal, Shankhadeep Han, Deguang Mohapatra, R. N. Functional Analysis 42C15, 47B02, 94A12 This paper explores the structure of optimal K-dual frames for a given K-frame and optimal K-dual pairs, within the context of erasures which occur during the transmission of frame coefficients. We address two distinct erasure scenarios and examine their impact on the reconstruction process. The optimality criteria are defined in terms of minimizing the spectral radius and the operator norm of the associated error operators. Through this approach, we provide a comprehensive framework for understanding and mitigating the effects of erasures in frame theory, contributing to enhanced robustness in data transmission and recovery. |
| title | Optimal K dual frames and pairs in the presence of erasures |
| topic | Functional Analysis 42C15, 47B02, 94A12 |
| url | https://arxiv.org/abs/2508.01964 |