Eigenvalue bounds for Schrödinger operators with complex potentials. II
Laptev and Safronov conjectured that any non-positive eigenvalue of a Schrödinger operator -Δ+V in L^2 (R^ν) with complex potential has absolute value at most a constant times ||V||^(γ+ν/2)/γ)_(γ+ν/2) for 0 < γ ≤ ν/2 in dimension ν ≥ 2. We prove this conjecture for radial potentials if 0 < γ &...
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European Mathematical Society
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ftcaltechauth:oai:authors.library.caltech.edu:77120 2023-05-15T17:07:15+02:00 Eigenvalue bounds for Schrödinger operators with complex potentials. II Frank, Rupert L. Simon, Barry 2017-09-28 application/pdf https://authors.library.caltech.edu/77120/ https://authors.library.caltech.edu/77120/1/1504.01144.pdf https://resolver.caltech.edu/CaltechAUTHORS:20170502-082840587 en eng European Mathematical Society https://authors.library.caltech.edu/77120/1/1504.01144.pdf Frank, Rupert L. and Simon, Barry (2017) Eigenvalue bounds for Schrödinger operators with complex potentials. II. Journal of Spectral Theory, 7 (3). pp. 633-658. ISSN 1664-039X. doi:10.4171/JST/173. https://resolver.caltech.edu/CaltechAUTHORS:20170502-082840587 <https://resolver.caltech.edu/CaltechAUTHORS:20170502-082840587> other Article PeerReviewed 2017 ftcaltechauth https://doi.org/10.4171/JST/173 2021-11-18T18:42:00Z Laptev and Safronov conjectured that any non-positive eigenvalue of a Schrödinger operator -Δ+V in L^2 (R^ν) with complex potential has absolute value at most a constant times ||V||^(γ+ν/2)/γ)_(γ+ν/2) for 0 < γ ≤ ν/2 in dimension ν ≥ 2. We prove this conjecture for radial potentials if 0 < γ < ν/2 and we ‘almost disprove’ it for general potentials if 1/2 < γ < ν/2. In addition, we prove various bounds that hold, in particular, for positive eigenvalues. Article in Journal/Newspaper laptev Caltech Authors (California Institute of Technology) Journal of Spectral Theory 7 3 633 658 |
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Caltech Authors (California Institute of Technology) |
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English |
description |
Laptev and Safronov conjectured that any non-positive eigenvalue of a Schrödinger operator -Δ+V in L^2 (R^ν) with complex potential has absolute value at most a constant times ||V||^(γ+ν/2)/γ)_(γ+ν/2) for 0 < γ ≤ ν/2 in dimension ν ≥ 2. We prove this conjecture for radial potentials if 0 < γ < ν/2 and we ‘almost disprove’ it for general potentials if 1/2 < γ < ν/2. In addition, we prove various bounds that hold, in particular, for positive eigenvalues. |
format |
Article in Journal/Newspaper |
author |
Frank, Rupert L. Simon, Barry |
spellingShingle |
Frank, Rupert L. Simon, Barry Eigenvalue bounds for Schrödinger operators with complex potentials. II |
author_facet |
Frank, Rupert L. Simon, Barry |
author_sort |
Frank, Rupert L. |
title |
Eigenvalue bounds for Schrödinger operators with complex potentials. II |
title_short |
Eigenvalue bounds for Schrödinger operators with complex potentials. II |
title_full |
Eigenvalue bounds for Schrödinger operators with complex potentials. II |
title_fullStr |
Eigenvalue bounds for Schrödinger operators with complex potentials. II |
title_full_unstemmed |
Eigenvalue bounds for Schrödinger operators with complex potentials. II |
title_sort |
eigenvalue bounds for schrödinger operators with complex potentials. ii |
publisher |
European Mathematical Society |
publishDate |
2017 |
url |
https://authors.library.caltech.edu/77120/ https://authors.library.caltech.edu/77120/1/1504.01144.pdf https://resolver.caltech.edu/CaltechAUTHORS:20170502-082840587 |
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laptev |
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laptev |
op_relation |
https://authors.library.caltech.edu/77120/1/1504.01144.pdf Frank, Rupert L. and Simon, Barry (2017) Eigenvalue bounds for Schrödinger operators with complex potentials. II. Journal of Spectral Theory, 7 (3). pp. 633-658. ISSN 1664-039X. doi:10.4171/JST/173. https://resolver.caltech.edu/CaltechAUTHORS:20170502-082840587 <https://resolver.caltech.edu/CaltechAUTHORS:20170502-082840587> |
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other |
op_doi |
https://doi.org/10.4171/JST/173 |
container_title |
Journal of Spectral Theory |
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7 |
container_issue |
3 |
container_start_page |
633 |
op_container_end_page |
658 |
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1766062602165682176 |