Opuscula Math. 36, no. 6 (2016), 769-786
http://dx.doi.org/10.7494/OpMath.2016.36.6.769

Opuscula Mathematica

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

Markus Holzleitner
Aleksey Kostenko
Gerald Teschl

Abstract. 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.

Keywords: Schrödinger equation, dispersive estimates, scattering.

Mathematics Subject Classification: 35Q41, 34L25, 81U30, 81Q15.

Full text (pdf)

• Markus Holzleitner
• University of Vienna, Faculty of Mathematics, Oskar-Morgenstern-Platz 1, 1090 Wien, Austria
• Aleksey Kostenko
• University of Vienna, Faculty of Mathematics, Oskar-Morgenstern-Platz 1, 1090 Wien, Austria
• Gerald Teschl
• University of Vienna, Faculty of Mathematics, Oskar-Morgenstern-Platz 1, 1090 Wien, Austria
• International Erwin Schrödinger Institute for Mathematical Physics, Boltzmanngasse 9, 1090 Wien, Austria
• Communicated by S.N. Naboko.
• Revised: 2016-05-12.
• Accepted: 2016-05-12.
• Published online: 2016-10-29.