2 citations · 2 across the 5 of their papers we have counts for
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Singular Schrödinger operators with prescribed spectral properties
Jussi Behrndt, Andrii Khrabustovskyi
The paper deals with singular Schrödinger operators of the form \begin{gather*} -{\mathrm{d}^2\over \mathrm{d} x^2 } + \sum_{k\in\mathbb{Z} }γ_k δ(\cdot-z_k),\quad γ_k\in\mathbb{R}…
Periodic quantum graphs with predefined spectral gaps
Andrii Khrabustovskyi
Let be an arbitrary -periodic metric graph, which does not coincide with a line. We consider the Hamiltonian on with the action $-\v…
Construction of self-adjoint differential operators with prescribed spectral properties
Jussi Behrndt, Andrii Khrabustovskyi
In this expository article some spectral properties of self-adjoint differential operators are investigated. The main objective is to illustrate and (partly) review how one can con…
-interaction as a limit of a thin Neumann waveguide with transversal window
Giuseppe Cardone, Andrii Khrabustovskyi
We consider a waveguide-like domain consisting of two thin straight tubular domains connected through a tiny window. The perpendicular size of this waveguide is of order $\varepsil…
Spectral estimates for Dirichlet Laplacian on tubes with exploding twisting velocity
Diana Barseghyan, Andrii Khrabustovskyi
We study the spectrum of the Dirichlet Laplacian on an unbounded twisted tube with twisting velocity exploding to infinity. If the tube cross section does not intersect the axis of…
Gap control by singular Schrödinger operators in a periodically structured metamaterial
Pavel Exner, Andrii Khrabustovskyi
We consider a family of -periodic Schrödinger operators with -interactions supported on a lattice of clos…