Datchev, K;
Galkowski, J;
Shapiro, J;
(2023)
Semiclassical resolvent bounds for compactly supported radial potentials.
Journal of Functional Analysis
, 284
(7)
, Article 109835. 10.1016/j.jfa.2022.109835.
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Abstract
We employ separation of variables to prove weighted resolvent estimates for the semi- classical Schrodinger operator −h2Δ + V (|x|) − E in dimension n ≥ 2, where h, E > 0, and V : [0, ∞) → R is L∞ and compactly supported. The weighted resolvent norm grows no faster than exp(Ch−1), while an exterior weighted norm grows ∼ h−1. We introduce a new method based on the Mellin transform to handle the two-dimensional case.
| Type: | Article |
|---|---|
| Title: | Semiclassical resolvent bounds for compactly supported radial potentials |
| Event: | AMS Spring Central Virtual Sectional Meeting, March 26-27, 2022 |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1016/j.jfa.2022.109835 |
| Publisher version: | https://doi.org/10.1016/j.jfa.2022.109835 |
| Language: | English |
| Additional information: | This version is the author accepted manuscript. For information on re-use, please refer to the publisher's terms and conditions. |
| Keywords: | Resolvent estimate, Schrödinger operator, Radial potential |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10141124 |
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