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

• Main Authors: Markus Holzleitner, Aleksey Kostenko, Gerald Teschl
• Format: Article
• Language: English
• Published: AGH Univeristy of Science and Technology Press 2016-01-01
• Series: Opuscula Mathematica
• Subjects: Schrödinger equation; dispersive estimates; scattering
• Online Access: http://www.opuscula.agh.edu.pl/vol36/6/art/opuscula_math_3646.pdf

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.