Schrödinger Operator with Non-Zero Accumulation Points of Complex Eigenvalues

Boegli, Sabine

doi:10.1007/s00220-016-2806-5

Schrödinger Operator with Non-Zero Accumulation Points of Complex Eigenvalues

Boegli, Sabine

Authors

Dr Sabine Boegli sabine.boegli@durham.ac.uk
Associate Professor

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.

Citation

Boegli, S. (2017). Schrödinger Operator with Non-Zero Accumulation Points of Complex Eigenvalues. Communications in Mathematical Physics, 352(2), 629-639. https://doi.org/10.1007/s00220-016-2806-5

Journal Article Type	Article
Acceptance Date	Oct 10, 2016
Online Publication Date	Nov 18, 2016
Publication Date	Jun 30, 2017
Deposit Date	Dec 11, 2019
Publicly Available Date	Dec 12, 2019
Journal	Communications in Mathematical Physics
Print ISSN	0010-3616
Electronic ISSN	1432-0916
Publisher	Springer
Peer Reviewed	Peer Reviewed
Volume	352
Issue	2
Pages	629-639
DOI	https://doi.org/10.1007/s00220-016-2806-5

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Copyright 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