Boegli, Sabine (2017) 'Schrödinger operator with non-zero accumulation points of complex eigenvalues.', Communications in mathematical physics., 352 (2). pp. 629-639.
Abstract
We study Schrödinger operators H=−Δ+V in L2(Ω) where Ω is Rd or the half-space Rd+, subject to (real) Robin boundary conditions in the latter case. For p>d we construct a non-real potential V∈Lp(Ω)∩L∞(Ω) that decays at infinity so that H has infinitely many non-real eigenvalues accumulating at every point of the essential spectrum σess(H)=[0,∞). This demonstrates that the Lieb–Thirring inequalities for selfadjoint Schrödinger operators are no longer true in the non-selfadjoint case.
| Item Type: | Article |
|---|---|
| Full text: | (AM) Accepted Manuscript Download PDF (311Kb) |
| Status: | Peer-reviewed |
| Publisher Web site: | https://doi.org/10.1007/s00220-016-2806-5 |
| Publisher statement: | This is a post-peer-review, pre-copyedit version of an article published in Communications in mathematical physics. The final authenticated version is available online at: https://doi.org/10.1007/s00220-016-2806-5 |
| Date accepted: | 10 October 2016 |
| Date deposited: | 12 December 2019 |
| Date of first online publication: | 18 November 2016 |
| Date first made open access: | 12 December 2019 |
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