Eigenvalue bounds for Schrödinger operators with complex potentials

We show that the absolute values of non-positive eigenvalues of Schrödinger operators with complex potentials can be bounded in terms of L_p-norms of the potential. This extends an inequality of Abramov, Aslanyan, and Davies to higher dimensions and proves a conjecture by Laptev and Safronov. Our ma...

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Main Author: Frank, Rupert L.
Format: Text
Language:unknown
Published: arXiv 2010
Subjects:
Spectral Theory math.SP
Mathematical Physics math-ph
FOS Mathematics
FOS Physical sciences
Sogge
laptev
Online Access:https://dx.doi.org/10.48550/arxiv.1005.2785
https://arxiv.org/abs/1005.2785
id ftdatacite:10.48550/arxiv.1005.2785
record_format openpolar
spelling ftdatacite:10.48550/arxiv.1005.2785 2023-05-15T17:07:14+02:00 Eigenvalue bounds for Schrödinger operators with complex potentials Frank, Rupert L. 2010 https://dx.doi.org/10.48550/arxiv.1005.2785 https://arxiv.org/abs/1005.2785 unknown arXiv https://dx.doi.org/10.1112/blms/bdr008 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 article-journal Article ScholarlyArticle Text 2010 ftdatacite https://doi.org/10.48550/arxiv.1005.2785 https://doi.org/10.1112/blms/bdr008 2022-04-01T14:22:36Z We show that the absolute values of non-positive eigenvalues of Schrödinger operators with complex potentials can be bounded in terms of L_p-norms of the potential. This extends an inequality of Abramov, Aslanyan, and Davies to higher dimensions and proves a conjecture by Laptev and Safronov. Our main ingredient are the uniform Sobolev inequalities of Kenig, Ruiz, and Sogge. : 7 pages Text laptev DataCite Metadata Store (German National Library of Science and Technology) Sogge ENVELOPE(7.724,7.724,62.529,62.529)
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
spellingShingle Spectral Theory math.SP
Mathematical Physics math-ph
FOS Mathematics
FOS Physical sciences
Frank, Rupert L.
Eigenvalue bounds for Schrödinger operators with complex potentials
topic_facet Spectral Theory math.SP
Mathematical Physics math-ph
FOS Mathematics
FOS Physical sciences
description We show that the absolute values of non-positive eigenvalues of Schrödinger operators with complex potentials can be bounded in terms of L_p-norms of the potential. This extends an inequality of Abramov, Aslanyan, and Davies to higher dimensions and proves a conjecture by Laptev and Safronov. Our main ingredient are the uniform Sobolev inequalities of Kenig, Ruiz, and Sogge. : 7 pages
format Text
author Frank, Rupert L.
author_facet Frank, Rupert L.
author_sort Frank, Rupert L.
title Eigenvalue bounds for Schrödinger operators with complex potentials
title_short Eigenvalue bounds for Schrödinger operators with complex potentials
title_full Eigenvalue bounds for Schrödinger operators with complex potentials
title_fullStr Eigenvalue bounds for Schrödinger operators with complex potentials
title_full_unstemmed Eigenvalue bounds for Schrödinger operators with complex potentials
title_sort eigenvalue bounds for schrödinger operators with complex potentials
publisher arXiv
publishDate 2010
url https://dx.doi.org/10.48550/arxiv.1005.2785
https://arxiv.org/abs/1005.2785
long_lat ENVELOPE(7.724,7.724,62.529,62.529)
geographic Sogge
geographic_facet Sogge
genre laptev
genre_facet laptev
op_relation https://dx.doi.org/10.1112/blms/bdr008
op_rights arXiv.org perpetual, non-exclusive license
http://arxiv.org/licenses/nonexclusive-distrib/1.0/
op_doi https://doi.org/10.48550/arxiv.1005.2785
https://doi.org/10.1112/blms/bdr008
_version_ 1766062564584718336

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