Opuscula Mathematica
Opuscula Math. 36, no. 6 (), 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




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
 
Download this article's citation as:
a .bib file (BibTeX), a .ris file (RefMan), a .enw file (EndNote)
or export to RefWorks.

RSS Feed

horizontal rule

ISSN 1232−9274, e-ISSN 2300−6919, DOI https://doi.org/10.7494/OpMath
Copyright © 2003−2017 OPUSCULA MATHEMATICA
Contact: opuscula@agh.edu.pl
Made by Tomasz Zabawa

horizontal rule

In accordance with EU legislation we advise you this website uses cookies to allow us to see how the site is used. All data is anonymized.
All recent versions of popular browsers give users a level of control over cookies. Users can set their browsers to accept or reject all, or certain, cookies.