Uncertainty principles

Signal processing/spectral uncertainties

TBD. see wikipedia for now.

Entropic uncertainty

where the “≈” indicates convergence in $L_2$, and normalized so that (by Plancherel's theorem),

He showed that for any such functions the sum of the Shannon entropies is non-negative,

was conjectured by Hirschman and Everett, proven in 1975 by Beckner and in the same year interpreted by as a generalized quantum mechanical uncertainty principle by Białynicki-Birula and Mycielski. The equality holds in the case of Gaussian distributions.