# Detecting Fourier Subspaces

@article{Akemann2015DetectingFS,
title={Detecting Fourier Subspaces},
author={C. Akemann and N. Weaver},
journal={Journal of Fourier Analysis and Applications},
year={2015},
volume={22},
pages={878-886}
}
• Published 2015
• Mathematics
• Journal of Fourier Analysis and Applications
• Let G be a finite abelian group. We examine the discrepancy between subspaces of $$l^2(G)$$l2(G) which are diagonalized in the standard basis and subspaces which are diagonalized in the dual Fourier basis. The general principle is that a Fourier subspace whose dimension is small compared to $$|G| = \mathrm{dim}\left( l^2(G)\right)$$|G|=diml2(G) tends to be far away from standard subspaces. In particular, the recent positive solution of the Kadison–Singer problem shows that from within any… CONTINUE READING