Abstract

Motivated by nonlinear problems, the dispersive estimates for the Schrodinger operators $H=-\Delta+V(x)$ have evoked considerable interest in the past three decades. In this talk, we investigate the stability of dispersive estimates under finite rank perturbations, which arise in a number of problems in mathematical physics. We improve previous related results by Nier and Soffer (J Funct. Anal. 198 (2003), 511-535). We mention that our approach is very different from the methods used by Nier and Soffer both in rank one and finite rank perturbations. Moreover, this approach relaxes the smoothness and decay assumption and works for all dimensions. This is joint work with Han Cheng and Quan Zheng.