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Frontiers of Mathematics in China

ISSN 1673-3452

ISSN 1673-3576(Online)

CN 11-5739/O1

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2018 Impact Factor: 0.565

Front. Math. China    2022, Vol. 17 Issue (4) : 501-509    https://doi.org/10.1007/s11464-022-1024-z
SURVEY ARTICLE
Linear independence of a finite set of time-frequency shifts
Dengfeng LI()
School of Mathematics and Physics Science, Wuhan Textile University, Wuhan 430200, China
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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.

Keywords Time-frequency shift      Gabor frame      wavelet      linear independence     
Online First Date: 09 December 2022    Issue Date: 19 December 2022
 Cite this article:   
Dengfeng LI. Linear independence of a finite set of time-frequency shifts[J]. Front. Math. China, 2022, 17(4): 501-509.
 URL:  
https://academic.hep.com.cn/fmc/EN/10.1007/s11464-022-1024-z
https://academic.hep.com.cn/fmc/EN/Y2022/V17/I4/501
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