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Linear independence of a finite set of time-frequency shifts

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Abstract

This paper introduces an open conjecture in time-frequency analysis on the linear independence of a finite set of time-frequency shifts of a given L2 function. Firstly, background and motivation for the conjecture are provided. Secondly, the main progress of this linear independence in the past twenty five years is reviewed. Finally, the partial results of the high dimensional case and other cases for the conjecture are briefly presented.

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Acknowledgements

This work was supported in part by the National Natural Science Foundation of China (Grant No. 61471410) and the Construction Fund for Subject Innovation Term of Wuhan Textile University (No. 201401023).

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Authors and Affiliations

  1. School of Mathematics and Physics Science, Wuhan Textile University, Wuhan, 430200, China

    Dengfeng Li

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  1. Dengfeng Li
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Correspondence to Dengfeng Li.

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Translated from Advances in Mathematics (China), 2022, 51(3):400–406

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Li, D. Linear independence of a finite set of time-frequency shifts. Front. Math. China 17, 501–509 (2022). https://doi.org/10.1007/s11464-022-1024-z

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