ﻻ يوجد ملخص باللغة العربية
We consider two-dimensional Schroedinger operators with an attractive potential in the form of a channel of a fixed profile built along an unbounded curve composed of a circular arc and two straight semi-lines. Using a test-function argument with help of parallel coordinates outside the cut-locus of the curve, we establish the existence of discrete eigenvalues. This is a special variant of a recent result of Exner in a non-smooth case and via a different technique which does not require non-positive constraining potentials.
We show that twisting of an infinite straight three-dimensional tube with non-circular cross-section gives rise to a Hardy-type inequality for the associated Dirichlet Laplacian. As an application we prove certain stability of the spectrum of the Dir
We consider the Dirichlet Laplacian in a straight three dimensional waveguide with non-rotationally invariant cross section, perturbed by a twisting of small amplitude. It is well known that such a perturbation does not create eigenvalues below the e
We describe some basic tools in the spectral theory of Schrodinger operator on metric graphs (also known as quantum graph) by studying in detail some basic examples. The exposition is kept as elementary and accessible as possible. In the later sectio
We briefly review the diffraction of quasicrystals and then give an elementary alternative proof of the diffraction formula for regular cut-and-project sets, which is based on Bochners theorem from Fourier analysis. This clarifies a common view that
Given two Hilbert spaces, $mathcal{H}$ and $mathcal{K}$, we introduce an abstract unitary operator $U$ on $mathcal{H}$ and its discriminant $T$ on $mathcal{K}$ induced by a coisometry from $mathcal{H}$ to $mathcal{K}$ and a unitary involution on $mat