Characterizations of weak R-duality and its application to Gabor frames
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866913481871065088 |
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| author | Bansal, Himanshi Devaraj, P. Arati, S. |
| author_facet | Bansal, Himanshi Devaraj, P. Arati, S. |
| contents | Weak R-duals, a generalization of R-duals, were recently introduced; for which duality relations were established. In this paper, we consider the problem of characterizing a given frame sequence to be a weak R-dual of a given frame. Further, we apply these characterization results to the Gabor frame setting and prove that the weak R-duality of the adjoint Gabor system leads to the R-duality of the same, thereby indicating an approach to answer the famous problem of the adjoint Gabor system being an R-dual of a given Gabor frame. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_14952 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Characterizations of weak R-duality and its application to Gabor frames Bansal, Himanshi Devaraj, P. Arati, S. Functional Analysis 42C15, 42C40, 41A58 Weak R-duals, a generalization of R-duals, were recently introduced; for which duality relations were established. In this paper, we consider the problem of characterizing a given frame sequence to be a weak R-dual of a given frame. Further, we apply these characterization results to the Gabor frame setting and prove that the weak R-duality of the adjoint Gabor system leads to the R-duality of the same, thereby indicating an approach to answer the famous problem of the adjoint Gabor system being an R-dual of a given Gabor frame. |
| title | Characterizations of weak R-duality and its application to Gabor frames |
| topic | Functional Analysis 42C15, 42C40, 41A58 |
| url | https://arxiv.org/abs/2408.14952 |