Schrödinger Operators with δ -potentials Supported on Unbounded Lipschitz Hypersurfaces

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61389005%3A_____%2F23%3A00576240" target="_blank" >RIV/61389005:_____/23:00576240 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1007/978-3-031-31139-0_8" target="_blank" >http://dx.doi.org/10.1007/978-3-031-31139-0_8</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/978-3-031-31139-0_8" target="_blank" >10.1007/978-3-031-31139-0_8</a>

Result language
angličtina
Original language name
Schrödinger Operators with δ -potentials Supported on Unbounded Lipschitz Hypersurfaces
Original language description
In this note we consider the self-adjoint Schrödinger operator Aα in L2(ℝd), d≥ 2, with a δ -potential supported on a Lipschitz hypersurface Σ ⊆ ℝd of strength α∈ Lp(Σ ) + L∞(Σ ). We show the uniqueness of the ground state and, under some additional conditions on the coefficient α and the hypersurface Σ, we determine the essential spectrum of Aα. In the special case that Σ is a hyperplane we obtain a Birman-Schwinger principle with a relativistic Schrödinger operator as Birman-Schwinger operator. As an application we prove an optimization result for the bottom of the spectrum of Aα.
Czech name
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Czech description
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Project
<a href="/en/project/GA21-07129S" target="_blank" >GA21-07129S: New Effects from Time-Reversal Non-Invariance</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2023
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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