Letters in Mathematical Physics

, Volume 106, Issue 2, pp 197–220 | Cite as

Estimates for Eigenvalues of Schrödinger Operators with Complex-Valued Potentials

  • Alexandra Enblom


New estimates for eigenvalues of non-self-adjoint multi-dimensional Schrödinger operators are obtained in terms of L p -norms of the potentials. The results cover and improve those known previously, in particular, due to Frank (Bull Lond Math Soc 43(4):745–750, 2011), Safronov (Proc Am Math Soc 138(6):2107–2112, 2010), Laptev and Safronov (Commun Math Phys 292(1):29–54, 2009). We mention the estimations of the eigenvalues situated in the strip around the real axis (in particular, the essential spectrum). The method applied for this case involves the unitary group generated by the Laplacian. The results are extended to the more general case of polyharmonic operators. Schrödinger operators with slowly decaying potentials and belonging to weak Lebesgue’s classes are also considered.


Schrödinger operators polyharmonic operators complex potential estimation of eigenvalues 

Mathematics Subject Classifications

Primary 47F05 Secondary 35P15 81Q12 


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© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  1. 1.Department of MathematicsLinköping UniversityLinköpingSweden

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