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 L1→ L 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∈ (0,1/2). However, for nonpositive angular momenta, l∈ (-1/2,0], the standard O(|t|-1/2) decay remains true for all self-adjoint realizations.

MSC2010: Primary 35Q41, 34L25; Secondary 81U30, 81Q15
Keywords: Schrödinger equation, dispersive estimates, scattering

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