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 &...
| Published in: | Journal of Spectral Theory |
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| Main Authors: | , |
| Format: | Article in Journal/Newspaper |
| Language: | English |
| Published: |
European Mathematical Society
2017
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| Subjects: | |
| Online Access: | https://authors.library.caltech.edu/77120/ https://authors.library.caltech.edu/77120/1/1504.01144.pdf https://resolver.caltech.edu/CaltechAUTHORS:20170502-082840587 |
| Summary: | 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. |
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