%0 Journal Article %T A revision of "On asymptotic stability in energy space of ground states of NLS in 1D" %A Scipio Cuccagna %J Mathematics %D 2007 %I arXiv %X We transpose work by T.Mizumachi to prove smoothing estimates for dispersive solutions of the linearization at a ground state of a Nonlinear Schr\"odinger equation (NLS) in 1D. As an application we extend to dimension 1D a result on asymptotic stability of ground states of NLS proved by Cuccagna & Mizumachi for dimensions $\ge 3$ %U http://arxiv.org/abs/0711.4192v3