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arXiv:0709.0517 [math.FA]AbstractReferencesReviewsResources

On the linear independence of spikes and sines

Joel A. Tropp

Published 2007-09-04, updated 2008-04-17Version 2

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 involves depends on an extrapolation argument of Bourgain and Tzafriri.

Comments: 16 pages, 4 figures. Revision with new proof of major theorems
Journal: J. Fourier Anal. Appl., Vol. 14, pp. 838-858, 2008
Categories: math.FA, math.MG
Subjects: 46B07, 47A11, 15A52
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