@inbook{367728de53af46c69fd1dbb3a2739d53,
title = "Schr{\"o}dinger Operators with δ -potentials Supported on Unbounded Lipschitz Hypersurfaces",
abstract = "In this note we consider the self-adjoint Schr{\"o}dinger 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 Schr{\"o}dinger operator as Birman-Schwinger operator. As an application we prove an optimization result for the bottom of the spectrum of Aα.",
keywords = "Birman-Schwinger operator, Eigenvalue optimization, Essential spectrum, Ground state, Schr{\"o}dinger operator, Singular potential",
author = "Jussi Behrndt and Vladimir Lotoreichik and Peter Schlosser",
note = "Publisher Copyright: {\textcopyright} 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.",
year = "2023",
doi = "10.1007/978-3-031-31139-0_8",
language = "English",
isbn = "978-3-031-31138-3",
series = "Operator Theory: Advances and Applications",
publisher = "Springer Science and Business Media Deutschland GmbH",
pages = "123--150",
booktitle = "From Complex Analysis to Operator Theory",
address = "Germany",
}