Operator Theory: Advances and Applications

0576240 - ÚJF 2024 RIV DE eng M - Část monografie knihy
Behrndt, J. - Lotoreichik, Vladimir - Schlosser, P.
Schrödinger Operators with δ -potentials Supported on Unbounded Lipschitz Hypersurfaces.
Operator Theory: Advances and Applications. Vol. 291. Cham: Birkhäuser, 2023, s. 123-150. ISBN 978-3-031-31138-3
Grant CEP: GA ČR(CZ) GA21-07129S
Institucionální podpora: RVO:61389005
Klíčová slova: Birman-Schwinger operator * Eigenvalue optimization * Essential spectrum * Ground state * Schrödinger operator * Singular potential
Obor OECD: Applied mathematics

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.
Trvalý link: https://hdl.handle.net/11104/0345816