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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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 |
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Caltech Authors (California Institute of Technology) |
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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> |
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other |
op_doi |
https://doi.org/10.1112/blms/bdr008 |
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Bulletin of the London Mathematical Society |
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43 |
container_issue |
4 |
container_start_page |
745 |
op_container_end_page |
750 |
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1766062515663405056 |