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.

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  • 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.
  • Received: 2016-01-07.
  • Revised: 2016-05-12.
  • Accepted: 2016-05-12.
  • Published online: 2016-10-29.
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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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