Sharp semiclassical spectral asymptotics for Schrödinger operators with non-smooth potentials
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866909308148514816 |
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| author | Mikkelsen, Søren |
| author_facet | Mikkelsen, Søren |
| contents | We consider semiclassical Schrödinger operators acting in $L^2(\mathbb{R}^d)$ with $d\geq3$. For these operators we establish a 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 one time differentiable and the derivative is Hölder continues with parameter $μ\geq1/2$. Moreover we also consider sharp Riesz means of order $γ$ with $γ\in(0,1]$. Here we assume the potential is locally integrable and that the negative part of the potential minus a constant is two time differentiable and the second derivative is Hölder continues with parameter $μ$ that depends on $γ$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_12015 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Sharp semiclassical spectral asymptotics for Schrödinger operators with non-smooth potentials Mikkelsen, Søren Spectral Theory Mathematical Physics We consider semiclassical Schrödinger operators acting in $L^2(\mathbb{R}^d)$ with $d\geq3$. For these operators we establish a 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 one time differentiable and the derivative is Hölder continues with parameter $μ\geq1/2$. Moreover we also consider sharp Riesz means of order $γ$ with $γ\in(0,1]$. Here we assume the potential is locally integrable and that the negative part of the potential minus a constant is two time differentiable and the second derivative is Hölder continues with parameter $μ$ that depends on $γ$. |
| title | Sharp semiclassical spectral asymptotics for Schrödinger operators with non-smooth potentials |
| topic | Spectral Theory Mathematical Physics |
| url | https://arxiv.org/abs/2309.12015 |