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• W3133303443 abstract "Abstract We establish quantitative upper and lower bounds for Schrödinger operators with complex potentials that satisfy some weak form of sparsity. Our first result is a quantitative version of an example, due to S. Bögli (Commun Math Phys 352:629–639, 2017), of a Schrödinger operator with eigenvalues accumulating to every point of the essential spectrum. The second result shows that the eigenvalue bounds of Frank (Bull Lond Math Soc 43:745–750, 2011 and Trans Am Math Soc 370:219–240, 2018) can be improved for sparse potentials. The third result generalizes a theorem of Klaus (Ann Inst H Poincaré Sect A (N.S.) 38:7–13, 1983) on the characterization of the essential spectrum to the multidimensional non-selfadjoint case. The fourth result shows that, in one dimension, the purely imaginary (non-sparse) step potential has unexpectedly many eigenvalues, comparable to the number of resonances. Our examples show that several known upper bounds are sharp." @default.
• W3133303443 created "2021-03-01" @default.
• W3133303443 creator A5075423235 @default.
• W3133303443 date "2022-04-05" @default.
• W3133303443 modified "2023-10-14" @default.
• W3133303443 title "Schrödinger Operators with Complex Sparse Potentials" @default.
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• W3133303443 doi "https://doi.org/10.1007/s00220-022-04358-1" @default.
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