Dispersion estimates for spherical Schrödinger equations: the effect of boundary conditions
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 di...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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AGH Univeristy of Science and Technology Press
2016-01-01
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| Series: | Opuscula Mathematica |
| Subjects: | |
| Online Access: | http://www.opuscula.agh.edu.pl/vol36/6/art/opuscula_math_3646.pdf |
| _version_ | 1811201838086619136 |
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| author | Markus Holzleitner Aleksey Kostenko Gerald Teschl |
| author_facet | Markus Holzleitner Aleksey Kostenko Gerald Teschl |
| author_sort | Markus Holzleitner |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-12T02:28:41Z |
| format | Article |
| id | doaj.art-43c283448fb94a97a25ae20d8ed767ce |
| institution | Directory Open Access Journal |
| issn | 1232-9274 |
| language | English |
| last_indexed | 2024-04-12T02:28:41Z |
| publishDate | 2016-01-01 |
| publisher | AGH Univeristy of Science and Technology Press |
| record_format | Article |
| series | Opuscula Mathematica |
| spelling | doaj.art-43c283448fb94a97a25ae20d8ed767ce2022-12-22T03:51:53ZengAGH Univeristy of Science and Technology PressOpuscula Mathematica1232-92742016-01-01366769786http://dx.doi.org/10.7494/OpMath.2016.36.6.7693646Dispersion estimates for spherical Schrödinger equations: the effect of boundary conditionsMarkus Holzleitner0Aleksey Kostenko1Gerald Teschl2University of Vienna, Faculty of Mathematics, Oskar-Morgenstern-Platz 1, 1090 Wien, AustriaUniversity of Vienna, Faculty of Mathematics, Oskar-Morgenstern-Platz 1, 1090 Wien, AustriaUniversity of Vienna, Faculty of Mathematics, Oskar-Morgenstern-Platz 1, 1090 Wien, AustriaWe 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.http://www.opuscula.agh.edu.pl/vol36/6/art/opuscula_math_3646.pdfSchrödinger equationdispersive estimatesscattering |
| spellingShingle | Markus Holzleitner Aleksey Kostenko Gerald Teschl Dispersion estimates for spherical Schrödinger equations: the effect of boundary conditions Opuscula Mathematica Schrödinger equation dispersive estimates scattering |
| title | Dispersion estimates for spherical Schrödinger equations: the effect of boundary conditions |
| title_full | Dispersion estimates for spherical Schrödinger equations: the effect of boundary conditions |
| title_fullStr | Dispersion estimates for spherical Schrödinger equations: the effect of boundary conditions |
| title_full_unstemmed | Dispersion estimates for spherical Schrödinger equations: the effect of boundary conditions |
| title_short | Dispersion estimates for spherical Schrödinger equations: the effect of boundary conditions |
| title_sort | dispersion estimates for spherical schrodinger equations the effect of boundary conditions |
| topic | Schrödinger equation dispersive estimates scattering |
| url | http://www.opuscula.agh.edu.pl/vol36/6/art/opuscula_math_3646.pdf |
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