18 papers
On an inverse dynamic problem for the wave equation with a potential on a real line
A. S. Mikhaylov, V. S. Mikhaylov
We consider the inverse dynamic problem for the wave equation with a potential on a real line. The forward initial-boundary value problem is set up with a help of boundary triplets…
On some applications of the Boundary Control method to spectral estimation and inverse problems
S. A. Avdonin, A. S. Mikhaylov, V. S. Mikhaylov
We consider applications of the Boundary Control (BC) method to generalized spectral estimation problems and to inverse source problems. We derive the equations of the BC method fo…
Inverse dynamic problems for canonical systems and de Branges spaces
A. S. Mikhaylov, V. S. Mikhaylov
We show the equivalence of inverse problems for different dynamical systems and corresponding canonical systems. For canonical system with general Hamiltonian we outline the strate…
On the construction of de Branges spaces for dynamical systems associated with finite Jacobi matrices
A. S. Mikhaylov, V. S. Mikhaylov
We consider dynamical systems with boundary control associated with finite Jacobi matrices. Using the method previously developed by the authors, we associate with these systems sp…
Dynamic inverse problem for complex Jacobi matrices
A. S. Mikhaylov, V. S. Mikhaylov
We consider the inverse dynamic problem for a dynamical system with discrete time associated with a semi-infinite complex Jacobi matrix. We propose two approaches of recovering coe…
Dynamical inverse problem for the discrete Schrödinger operator
A. S. Mikhaylov
We consider the inverse problem for the dynamical system with discrete Schrödinger operator and discrete time. As an inverse data we take a \emph{response operator}, the natural a…