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Schrödinger operator with non-zero accumulation points of complex eigenvalues.

Boegli, Sabine (2017) 'Schrödinger operator with non-zero accumulation points of complex eigenvalues.', Communications in mathematical physics., 352 (2). pp. 629-639.


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
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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:
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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