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}
}
  • C. Akemann, N. Weaver
  • 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

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