DISPERSION ESTIMATES FOR SPHERICAL SCHRODINGER EQUATIONS: THE EFFECT OF BOUNDARY CONDITIONS

We investigate the dependence of the L-1 -> L-infinity dispersive estimates for one-dimensional radial Schrodinger operators on boundary conditions at 0. In contrast to the case of additive perturbations, we show that the change of a boundary condition at zero results in the change of the dispersive decay estimates if the angular momentum is positive, l is an element of (0, 1/2). However, for nonpositive angular momenta, l is an element of(-1/2, 0], the standard O(vertical bar t vertical bar(-1/2)) decay remains true for all self-adjoint realizations.