[Banach] Abstract of a paper by Afonso S. Bandeira, Dustin G. Mixon, and Joel Moreira

This is an announcement for the paper "A conditional construction of restricted isometries" by Afonso S. Bandeira, Dustin G. Mixon, and Joel Moreira.

Abstract: We study the restricted isometry property of a matrix that is built from the discrete Fourier transform matrix by collecting rows indexed by quadratic residues. We find an $\epsilon>0$ such that, conditioned on a folklore conjecture in number theory, this matrix satisfies the restricted isometry property with sparsity parameter $K=\Omega(M^{1/2+\epsilon})$, where $M$ is the number of rows.

Archive classification: math.FA cs.IT math.IT math.NT

Remarks: 6 pages

Submitted from: moreira@math.ohio-state.edu

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1410.6457

or

http://arXiv.org/abs/1410.6457