Dispersive Estimates for Schrödinger Equations

The importance of the dispersive estimates for Schrödinger equations in spectral theory and in nonlinear analysis will be discussed. Furthermore, the literature on the $L^p-L^{p'}$ estimates will be reviewed, starting with the early results in the 1990 th, and with an emphasis in the results in one dimension. New results will be presented, in $L^p-L^{p'}$ estimates for matrix Schrödinger equations in the half-line, with general selfadjoint boundary condition, and in matrix Schrödinger equations in the full-line with point interactions. In both cases we consider integrable matrix potentials that have a finite first moment.