5 papers
On the absolutely continuous spectrum in a model of irreversible quantum graph
Sergey N. Naboko, Michael Solomyak
A family of differential operators depending on a real parameter is considered. This family was suggested by Smilansky as a model of an irreversible quantum system.…
On the discrete spectrum of a family of differential operators
Michael Solomyak
A family $\BA_\a$ of differential operators depending on a real parameter $\a$ is considered. The problem can be formulated in the language of perturbation theory of quadratic form…
On approximation of functions from Sobolev spaces on metric graphs
Michael Solomyak
Some results on the approximation of functions from the Sobolev spaces on metric graphs by step functions are obtained. The estimates are uniform with respect to all graphs of a gi…
On the eigenvalue estimates for the weighted Laplacian on metric graphs
Michael Solomyak
Eigenvalue behavior for the equation -λy"=Vu on the edges of a graph G of final total length, with a non-negative weight function V and under the Kirchhoff matching conditions at t…
Laplace and Schrödinger operators on regular metric trees: the discrete spectrum case
Michael Solomyak
The Schrödinger operator on a metric tree is a family of ordinary differential operators on its edges complemented by certain matching conditions at the vertices. The regular trees…