@article{e5f415a5c95645f2a86035d9cc6b3644,
title = "Pseudomodes for Schr{\"o}dinger operators with complex potentials",
abstract = "For one-dimensional Schr{\"o}dinger operators with complex-valued potentials, we construct pseudomodes corresponding to large pseudoeigenvalues. We develop a first systematic non-semi-classical approach, which results in a substantial progress in achieving optimal conditions and conclusions as well as in covering a wide class of previously inaccessible potentials, including discontinuous ones. Applications of the present results to higher-dimensional Schr{\"o}dinger operators are also discussed.",
keywords = "Complex potential, Pseudospectrum, Schr{\"o}dinger operators, WKB",
author = "David Krej{\v c}i{\v r}{\'i}k and Petr Siegl",
note = "Funding Information: The authors would like to express their gratitude to the American Institute of Mathematics (AIM) for a support to organise the workshop [1] , which partially stimulated the present research. D.K. was partially supported by the GACR grant No. 18-08835S . Until December 2017, the research of P.S. was supported by the Swiss National Science Foundation , SNF Ambizione grant No. PZ00P2_154786 . Funding Information: The authors would like to express their gratitude to the American Institute of Mathematics (AIM) for a support to organise the workshop [1], which partially stimulated the present research. D.K. was partially supported by the GACR grant No. 18-08835S. Until December 2017, the research of P.S. was supported by the Swiss National Science Foundation, SNF Ambizione grant No. PZ00P2_154786. Publisher Copyright: {\textcopyright} 2018 Elsevier Inc.",
year = "2019",
month = may,
day = "1",
doi = "10.1016/j.jfa.2018.10.004",
language = "English",
volume = "276",
pages = "2856--2900",
journal = "Journal of Functional Analysis",
issn = "0022-1236",
publisher = "Academic Press",
number = "9",
}