The well-known ∣supp(f)∣∣supp(f∣≥∣G∣ inequality gives lower
estimation of each supports. In the present paper we give upper estimation
under arithmetic constrains. The main notion will be the additive energy which
plays a central role in additive combinatorics. We prove an uncertainty
inequality that shows a trade-off between the total changes of the indicator
function of a subset A⊆F2n and the additive energy of A
and the Fourier spectrum.Comment: 8 pages, Submitted to the journal "ADAM" in December 202