Semiclassical asymptotics for a class of singular Schrödinger operators

Let $Ω\subset \mathbb{R}^d$ be bounded with $C^1$ boundary. In this paper we consider Schrödinger operators $-Δ+ W$ on $Ω$ with $W(x)\approx\mathrm{dist}(x, \partialΩ)^{-2}$ as $\mathrm{dist}(x, \partialΩ)\to 0$. Under weak assumptions on $W$ we derive a two-term asymptotic formula for the sum of th...

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Bibliographic Details
Main Authors: Frank, Rupert L., Larson, Simon
Format: Article in Journal/Newspaper
Language:unknown
Published: arXiv 2020
Subjects:
Spectral Theory math.SP
Mathematical Physics math-ph
FOS Mathematics
FOS Physical sciences
35P20
Ari
laptev
Online Access:https://dx.doi.org/10.48550/arxiv.2010.05417
https://arxiv.org/abs/2010.05417
id ftdatacite:10.48550/arxiv.2010.05417
record_format openpolar
spelling ftdatacite:10.48550/arxiv.2010.05417 2023-05-15T17:07:15+02:00 Semiclassical asymptotics for a class of singular Schrödinger operators Frank, Rupert L. Larson, Simon 2020 https://dx.doi.org/10.48550/arxiv.2010.05417 https://arxiv.org/abs/2010.05417 unknown arXiv arXiv.org perpetual, non-exclusive license http://arxiv.org/licenses/nonexclusive-distrib/1.0/ Spectral Theory math.SP Mathematical Physics math-ph FOS Mathematics FOS Physical sciences 35P20 Article CreativeWork article Preprint 2020 ftdatacite https://doi.org/10.48550/arxiv.2010.05417 2022-03-10T15:06:02Z Let $Ω\subset \mathbb{R}^d$ be bounded with $C^1$ boundary. In this paper we consider Schrödinger operators $-Δ+ W$ on $Ω$ with $W(x)\approx\mathrm{dist}(x, \partialΩ)^{-2}$ as $\mathrm{dist}(x, \partialΩ)\to 0$. Under weak assumptions on $W$ we derive a two-term asymptotic formula for the sum of the eigenvalues of such operators. : Dedicated to Ari Laptev on the occasion of his 70th birthday Article in Journal/Newspaper laptev DataCite Metadata Store (German National Library of Science and Technology) Ari ENVELOPE(147.813,147.813,59.810,59.810)
institution Open Polar
collection DataCite Metadata Store (German National Library of Science and Technology)
op_collection_id ftdatacite
language unknown
topic Spectral Theory math.SP
Mathematical Physics math-ph
FOS Mathematics
FOS Physical sciences
35P20
spellingShingle Spectral Theory math.SP
Mathematical Physics math-ph
FOS Mathematics
FOS Physical sciences
35P20
Frank, Rupert L.
Larson, Simon
Semiclassical asymptotics for a class of singular Schrödinger operators
topic_facet Spectral Theory math.SP
Mathematical Physics math-ph
FOS Mathematics
FOS Physical sciences
35P20
description Let $Ω\subset \mathbb{R}^d$ be bounded with $C^1$ boundary. In this paper we consider Schrödinger operators $-Δ+ W$ on $Ω$ with $W(x)\approx\mathrm{dist}(x, \partialΩ)^{-2}$ as $\mathrm{dist}(x, \partialΩ)\to 0$. Under weak assumptions on $W$ we derive a two-term asymptotic formula for the sum of the eigenvalues of such operators. : Dedicated to Ari Laptev on the occasion of his 70th birthday
format Article in Journal/Newspaper
author Frank, Rupert L.
Larson, Simon
author_facet Frank, Rupert L.
Larson, Simon
author_sort Frank, Rupert L.
title Semiclassical asymptotics for a class of singular Schrödinger operators
title_short Semiclassical asymptotics for a class of singular Schrödinger operators
title_full Semiclassical asymptotics for a class of singular Schrödinger operators
title_fullStr Semiclassical asymptotics for a class of singular Schrödinger operators
title_full_unstemmed Semiclassical asymptotics for a class of singular Schrödinger operators
title_sort semiclassical asymptotics for a class of singular schrödinger operators
publisher arXiv
publishDate 2020
url https://dx.doi.org/10.48550/arxiv.2010.05417
https://arxiv.org/abs/2010.05417
long_lat ENVELOPE(147.813,147.813,59.810,59.810)
geographic Ari
geographic_facet Ari
genre laptev
genre_facet laptev
op_rights arXiv.org perpetual, non-exclusive license
http://arxiv.org/licenses/nonexclusive-distrib/1.0/
op_doi https://doi.org/10.48550/arxiv.2010.05417
_version_ 1766062590416388096

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