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Semiclassical resolvent bounds for compactly supported radial potentials

Galkowski, JE; Datchev, K; Shapiro, J; (2022) Semiclassical resolvent bounds for compactly supported radial potentials. arXiv (In press).

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Abstract

We employ separation of variables to prove weighted resolvent estimates for the semiclassical Schrödinger operator −h2Δ+V(|x|)−E in dimension n≥2, where h,E>0, and V:[0,∞)→ℝ is L∞ and compactly supported. We show that the weighted resolvent estimate grows no faster than exp(Ch−1), and prove an exterior weighted estimate which grows ∼h−1.

Type: Article
Title: Semiclassical resolvent bounds for compactly supported radial potentials
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.
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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