ﻻ يوجد ملخص باللغة العربية
We investigate the distribution of the resonances near spectral thresholds of Laplace operators on regular tree graphs with $k$-fold branching, $k geq 1$, perturbed by nonself-adjoint exponentially decaying potentials. We establish results on the absence of resonances which in particular involve absence of discrete spectrum near some sectors of the essential spectrum of the operators.
We describe the spectral theory of the adjacency operator of a graph which is isomorphic to homogeneous trees at infinity. Using some combinatorics, we reduce the problem to a scattering problem for a finite rank perturbation of the adjacency operato
From the viewpoint of quantum walks, the Ihara zeta function of a finite graph can be said to be closely related to its evolution matrix. In this note we introduce another kind of zeta function of a graph, which is closely related to, as to say, the
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 provide a purely variational proof of the existence of eigenvalues below the bottom of the essential spectrum for the Schrodinger operator with an attractive $delta$-potential supported by a star graph, i.e. by a finite union of rays emanating fro