Optimal dual pairs of frames for erasures
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866910756131307520 |
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| author | Arati, S. Devaraj, P. Mondal, Shankhadeep |
| author_facet | Arati, S. Devaraj, P. Mondal, Shankhadeep |
| contents | The study involves characterizations of dual pairs of frames which are optimal to handle erasures among all dual pairs for a finite dimensional Hilbert space. A new optimality measure using the Frobenius norm of the error operator has been introduced and the corresponding optimal dual pairs have been analyzed for any number of erasures. Also, other measures of the error operator, namely the spectral radius and the numerical radius, have been considered for the analysis. Besides, explicit construction of certain optimal dual pairs has been provided. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_15709 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Optimal dual pairs of frames for erasures Arati, S. Devaraj, P. Mondal, Shankhadeep Functional Analysis 42C15, 46C05, 15A60 The study involves characterizations of dual pairs of frames which are optimal to handle erasures among all dual pairs for a finite dimensional Hilbert space. A new optimality measure using the Frobenius norm of the error operator has been introduced and the corresponding optimal dual pairs have been analyzed for any number of erasures. Also, other measures of the error operator, namely the spectral radius and the numerical radius, have been considered for the analysis. Besides, explicit construction of certain optimal dual pairs has been provided. |
| title | Optimal dual pairs of frames for erasures |
| topic | Functional Analysis 42C15, 46C05, 15A60 |
| url | https://arxiv.org/abs/2412.15709 |