Abstract
We prove that an overcomplete Gabor frame in \({\ell }^2({\mathbb {Z}})\) generated by a finitely supported sequence is always linearly dependent. This is a particular case of a general result about linear dependence versus independence for Gabor systems in \({\ell }^2({\mathbb {Z}})\) with modulation parameter 1 / M and translation parameter N for some \(M,N\in {\mathbb {N}},\) and generated by a finite sequence g in \({\ell }^2({\mathbb {Z}})\) with K nonzero entries.
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The authors would like to thank Guido Janssen, Chris Heil and Shahaf Nitzan for useful comments and references.
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Communicated by A.J.E.M. Janssen.
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Christensen, O., Hasannasab, M. Gabor Frames in \({\ell }^2({\mathbb {Z}})\) and Linear Dependence. J Fourier Anal Appl 25, 101–107 (2019). https://doi.org/10.1007/s00041-017-9572-4
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DOI: https://doi.org/10.1007/s00041-017-9572-4