Dispersion Estimates for Spherical Schrödinger Equations: The Effect of Boundary Conditions

We investigate the dependence of the \(L^1\to L^\infty\) dispersive estimates for one-dimensional radial Schr\"o\-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...

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Bibliographic Details
Published in:arXiv.org 2016-10
Main Authors: Holzleitner, Markus, Kostenko, Aleksey, Teschl, Gerald
Format: Article
Language:English
Subjects:
Angular momentum
Boundary conditions
Decay
Dependence
Dispersion
Estimates
Schrodinger equation
Online Access:Get full text
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Summary:We investigate the dependence of the \(L^1\to L^\infty\) dispersive estimates for one-dimensional radial Schr\"o\-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.
ISSN:2331-8422
DOI:10.48550/arxiv.1601.01638