Dispersion estimates for spherical Schrödinger equations - the effect of boundary conditions

Abstract

We investigate the dependence of the $L^1\to L^{\infty}$ dispersive estimates for one-dimensional radial Schrödinger 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, $l\in (0,1/2)$. However, for nonpositive angular momenta, $l\in (-1/2,0]$, the standard $O(|t|^{-1/2})$ decay remains true for all self-adjoint realizations.