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 mai...

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Bibliographic Details
Published in:Bulletin of the London Mathematical Society
Main Author: Frank, Rupert L.
Format: Article in Journal/Newspaper
Language:English
Published: Wiley 2011
Subjects:
Sogge
laptev
Online Access:https://authors.library.caltech.edu/77079/
https://authors.library.caltech.edu/77079/1/1005.2785.pdf
https://resolver.caltech.edu/CaltechAUTHORS:20170501-065723391
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spelling ftcaltechauth:oai:authors.library.caltech.edu:77079 2023-05-15T17:07:13+02:00 Eigenvalue bounds for Schrödinger operators with complex potentials Frank, Rupert L. 2011-08 application/pdf https://authors.library.caltech.edu/77079/ https://authors.library.caltech.edu/77079/1/1005.2785.pdf https://resolver.caltech.edu/CaltechAUTHORS:20170501-065723391 en eng Wiley https://authors.library.caltech.edu/77079/1/1005.2785.pdf Frank, Rupert L. (2011) Eigenvalue bounds for Schrödinger operators with complex potentials. Bulletin of the London Mathematical Society, 43 (4). pp. 745-750. ISSN 0024-6093. doi:10.1112/blms/bdr008. https://resolver.caltech.edu/CaltechAUTHORS:20170501-065723391 <https://resolver.caltech.edu/CaltechAUTHORS:20170501-065723391> other Article PeerReviewed 2011 ftcaltechauth https://doi.org/10.1112/blms/bdr008 2021-11-18T18:42:00Z 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. Article in Journal/Newspaper laptev Caltech Authors (California Institute of Technology) Sogge ENVELOPE(7.724,7.724,62.529,62.529) Bulletin of the London Mathematical Society 43 4 745 750
institution Open Polar
collection Caltech Authors (California Institute of Technology)
op_collection_id ftcaltechauth
language English
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.
format Article in Journal/Newspaper
author Frank, Rupert L.
spellingShingle Frank, Rupert L.
Eigenvalue bounds for Schrödinger operators with complex potentials
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 Wiley
publishDate 2011
url https://authors.library.caltech.edu/77079/
https://authors.library.caltech.edu/77079/1/1005.2785.pdf
https://resolver.caltech.edu/CaltechAUTHORS:20170501-065723391
long_lat ENVELOPE(7.724,7.724,62.529,62.529)
geographic Sogge
geographic_facet Sogge
genre laptev
genre_facet laptev
op_relation https://authors.library.caltech.edu/77079/1/1005.2785.pdf
Frank, Rupert L. (2011) Eigenvalue bounds for Schrödinger operators with complex potentials. Bulletin of the London Mathematical Society, 43 (4). pp. 745-750. ISSN 0024-6093. doi:10.1112/blms/bdr008. https://resolver.caltech.edu/CaltechAUTHORS:20170501-065723391 <https://resolver.caltech.edu/CaltechAUTHORS:20170501-065723391>
op_rights other
op_doi https://doi.org/10.1112/blms/bdr008
container_title Bulletin of the London Mathematical Society
container_volume 43
container_issue 4
container_start_page 745
op_container_end_page 750
_version_ 1766062515663405056

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