41 citations · 158 across the 15 of their papers we have counts for
16 papers
Synthesis of a quantum tree Weyl matrix
Sergei A. Avdonin, Kira V. Khmelnytskaya, Vladislav V. Kravchenko
A method for successive synthesis of a Weyl matrix (or Dirichlet-to-Neumann map) of an arbitrary quantum tree is proposed. It allows one, starting from one boundary edge, to comput…
Reconstruction techniques for quantum trees
Sergei A. Avdonin, Kira V. Khmelnytskaya, Vladislav V. Kravchenko
The inverse problem of recovery of a potential on a quantum tree graph from Weyl's matrix given at a number of points is considered. A method for its numerical solution is proposed…
Recovery of a potential on a quantum star graph from Weyl's matrix
Sergei A. Avdonin, Kira V. Khmelnytskaya, Vladislav V. Kravchenko
The problem of recovery of a potential on a quantum star graph from Weyl's matrix given at a finite number of points is considered. A method for its approximate solution is propose…
A representation of the transmutation kernels for the Schrödinger operator in terms of eigenfunctions and applications
Kira V. Khmelnytskaya, Vladislav V. Kravchenko, Sergii M. Torba
The representations of the kernels of the transmutation operator and of its inverse relating the one-dimensional Schrödinger operator with the second derivative are obtained in ter…
Transmutation operators: construction and applications
Vladislav V. Kravchenko, Sergii M. Torba, Kira V. Khmelnytskaya
Recent results on the construction and applications of the transmutation (transformation) operators are discussed. Three new representations for solutions of the one-dimensional Sc…
Modulated electromagnetic fields in inhomogeneous media, hyperbolic pseudoanalytic functions and transmutations
Kira V. Khmelnytskaya, Vladislav V. Kravchenko, Sergii M. Torba
The time-dependent Maxwell system describing electromagnetic wave propagation in inhomogeneous isotropic media in the one-dimensional case reduces to a Vekua-type equation for bico…