On the linear independence of spikes and sines

Details On the linear independence of spikes and sines On the linear independence of spikes and sines

2007-09-04

arxiv.org/abs/0709.0517v2

J. Fourier Anal. Appl., Vol. 14, pp. 838-858, 2008

Mathematics

Functional Analysis

16 pages, 4 figures. Revision with new proof of major theorems

Scientific paper

10.1007/s00041-008-9042-0

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.

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