Sharp semiclassical spectral asymptotics for Schrödinger operators with non-smooth potentials
Year: 2025
Type: article
Abstract: We consider semiclassical Schrödinger operators acting in L^{2}(\mathbb{R}^{d}) with d\geq3 . For these operators, we establish sharp spectral asymptotics without full regularity. For the counting function, we assume the potential is locally integrable and that the negative part of the potential minus a constant is once differentiable, with its derivative being Hölder continuous with parameter \mu\geq1/2 . Moreover, we also consider sharp Riesz means of order \gamma with \gamma\in(0,1] . Here, we assume the potential is locally integrable and that the negative part of the potential minus a constant is twice differentiable, with its second derivative being Hölder continuous with parameter \mu that depends on \gamma .
Source: Journal of Spectral Theory
DOI: 10.4171/jst/557
Author: Søren Mikkelsen
Institution: University of Helsinki
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
Funder: Leverhulme Trust
OpenAlex ID: W4410191229