Schrödinger operator with a complex steplike potential

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21340%2F25%3A00377974" target="_blank" >RIV/68407700:21340/25:00377974 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1016/j.jde.2024.09.055" target="_blank" >https://doi.org/10.1016/j.jde.2024.09.055</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.jde.2024.09.055" target="_blank" >10.1016/j.jde.2024.09.055</a>

Result language
angličtina
Original language name
Schrödinger operator with a complex steplike potential
Original language description
The purpose of this article is to study pseudospectral properties of the one-dimensional Schrödinger operator perturbed by a complex steplike potential. By constructing the resolvent kernel, we show that the pseudospectrum of this operator is trivial if and only if the imaginary part of the potential is constant. As a by-product, a new method to obtain a sharp resolvent estimate is developed, answering a concern of Henry and Krejčiřík, and a way to construct an optimal pseudomode is discovered, answering a concern of Krejčiřík and Siegl. This article also analyzes the impact of a complex point interaction on the spectrum and the resolvent norm.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/GX20-17749X" target="_blank" >GX20-17749X: New challenges for spectral theory: geometry, advanced materials and complex fields</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2025
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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