Article

**Opuscula Math. 36, 769-786 (2016)**[DOI: 10.7494/OpMath.2016.36.6.769]

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

### Markus Holzleitner, Aleksey Kostenko, and Gerald Teschl

We investigate the dependence of the

*L*dispersive estimates for one-dimensional radial Schrödinger operators on boundary conditions at^{1}→ L^{∞}*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∈ (0,1/2)*. However, for nonpositive angular momenta,*l∈ (-1/2,0]*, the standard*O(|t|*decay remains true for all self-adjoint realizations.^{-1/2})
** MSC2010:** Primary 35Q41, 34L25; Secondary 81U30, 81Q15

**Keywords:** *Schrödinger equation, dispersive estimates, scattering*

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