arXiv subjects

Olga Boyko

Publications and source records attributed to Olga Boyko.

3 recordsLinked to original sources

arXiv2025

Recovering the shape of a quantum tree by scattering data

We consider a scattering problem generated by the Sturm-Liouville equation on a tree which consists of an equilateral compact subtree and a half-infinite lead attached to its root. We assume that the potential on the lead is identically zero while the potentials on the finite edges are real. We show how to find the shape of the tree using the S-function of the scattering problem and the eigenvalues of the operators associated with the compact tree.

math.FA↗

arXiv2022

On recovering the shape of a quantum tree from the spectrum of the Dirichlet boundary problem

Spectral problems are considered generated by the Sturm-Liouville equation on equilateral trees with the Dirichlet boundary conditions at the pendant vertices and continuity and Kirchhoff's conditions at the interior vertices. It is proved that there are no co-spectral (i.e., having the same spectrum of such problem) among equilateral trees of less or equal 8 vertices. All co-spectral trees of 9 vertices are presented.

math-ph↗

arXiv2018

On spectra of quadratic operator pencils with rank one gyroscopic linear part

The spectrum of a selfadjoint quadratic operator pencil of the form $λ^2M-λG-A$ is investigated where $M\geq 0$, $G\geq 0$ are bounded operators and $A$ is selfadjoint bounded below is investigated. It is shown that in the case of rank one operator $G$ the eigenvalues of such a pencil are of two types. The eigenvalues of one of these types are independent of the operator $G$. Location of the eigenvalues of both types is described. Examples for the case of the Sturm-Liouville operators $A$ are given.

math-ph↗