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arXiv · 2408.14952

Characterizations of weak R-duality and its application to Gabor frames

Himanshi Bansal·P. Devaraj·S. Arati
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Abstract

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.

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Himanshi Bansal, P. Devaraj, S. Arati. 2024-08-27. Characterizations of weak R-duality and its application to Gabor frames. https://arxiv.org/abs/2408.14952

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