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On the Linear Independence of Spikes and Sines

Tropp, Joel A. (2008) On the Linear Independence of Spikes and Sines. Journal of Fourier Analysis and Applications, 14 (5-6). pp. 838-858. ISSN 1069-5869. https://resolver.caltech.edu/CaltechAUTHORS:TROjfaa08

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Abstract

The purpose of this work is to survey what is known about the linear independence of spikes and sines. The paper provides new results for the case where the locations of the spikes and the frequencies of the sines are chosen at random. This problem is equivalent to studying the spectral norm of a random submatrix drawn from the discrete Fourier transform matrix. The proof depends on an extrapolation argument of Bourgain and Tzafriri.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1007/s00041-008-9042-0DOIArticle
https://rdcu.be/5jioPublisherFree ReadCube access
https://arxiv.org/abs/0709.0517arXivDiscussion Paper
ORCID:
AuthorORCID
Tropp, Joel A.0000-0003-1024-1791
Additional Information:© 2008 Springer. Received: 4 September 2007. Published online: 17 September 2008. Communicated by Anna Gilbert. One of the anonymous referees provided a wealth of useful advice that substantially improved the quality of this work. In particular, the referee described a version of Lemma 15 and demonstrated that it offers a simpler route to the main results than the argument in earlier drafts of this paper. Supported by NSF 0503299.
Funders:
Funding AgencyGrant Number
NSFDMS-0503299
Subject Keywords:Fourier analysis; Local theory; Random matrix; Sparse approximation; Uncertainty principle
Issue or Number:5-6
Record Number:CaltechAUTHORS:TROjfaa08
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:TROjfaa08
Official Citation:Tropp, J.A. J Fourier Anal Appl (2008) 14: 838. https://doi.org/10.1007/s00041-008-9042-0
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:12851
Collection:CaltechAUTHORS
Deposited By: Archive Administrator
Deposited On:08 Jan 2009 21:34
Last Modified:03 Oct 2019 00:32

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