Opuscula Mathematica
Opuscula Math. 36, no. 6 (), 769-786
Opuscula Mathematica

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

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.
Cite this article as:
Markus Holzleitner, Aleksey Kostenko, Gerald Teschl, Dispersion estimates for spherical Schrödinger equations: the effect of boundary conditions, Opuscula Math. 36, no. 6 (2016), 769-786, http://dx.doi.org/10.7494/OpMath.2016.36.6.769
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ISSN 1232−9274, e-ISSN 2300−6919, DOI https://doi.org/10.7494/OpMath
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