The aim of this article is to obtain a lower bound for the variance of a normalised $L^2$ function on the Heisenberg group under the assumption that its Fourier transform is small along a sequence of well distributed rays in the Heisenberg fan. This is achieved by proving an uncertainty inequality for Laguerre series which is analogous to the one obtained by Strichartz for spherical harmonic expansions. Applications to Hermite and special Hermite expansions are also given.
"On Strichartz's uncertainty inequality for the Heisenberg group." Tohoku Math. J. (2) 55 (3) 451 - 466, 2003. https://doi.org/10.2748/tmj/1113247483