Estimates for Eigenvalues of Schrodinger Operators with Complex-Valued Potentials

New estimates for eigenvalues of non-self-adjoint multi-dimensional Schrodinger 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 13...

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Bibliographic Details
Published in:Letters in Mathematical Physics
Main Author: Enblom, Alexandra
Format: Article in Journal/Newspaper
Language:English
Published: Linköpings universitet, Matematik och tillämpad matematik 2016
Subjects:
Schrodinger operators
polyharmonic operators
complex potential
estimation of eigenvalues
Mathematics
Matematik
laptev
Online Access:http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-125143
https://doi.org/10.1007/s11005-015-0810-x
Description
Summary:New estimates for eigenvalues of non-self-adjoint multi-dimensional Schrodinger 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. Schrodinger operators with slowly decaying potentials and belonging to weak Lebesgues classes are also considered.

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