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 Schrö\-din\-ger 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.

14 pages

Cited by in corpus (2)

• Transformation operators for spherical Schrödinger operators
• $L^p-L^{p^{\prime }}$ estimates for matrix Schrödinger equations