15 citations · 91 across the 22 of their papers we have counts for
22 papers
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…
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 an…
Forward and inverse problems for a finite Krein-Stieltjes string. Approximation of constant density by point masses
A. S. Mikhaylov, V. S. Mikhaylov
We consider a dynamic inverse problem for a dynamical system which describes the propagation of waves in a Krein string. The problem is reduced to an integral equation and an impor…
Inverse dynamic problem for the wave equation with periodic boundary conditions
A. S. Mikhaylov, V. S. Mikhaylov
We consider the inverse dynamic problem for the wave equation with a potential on an interval with periodic boundary conditions. We use a boundary triplet to set up the in…
One dimensional inverse problem in photoacoustic. Numerical testing
D. Langemann, A. S. Mikhaylov, V. S. Mikhaylov
We consider the problem of reconstruction of Cauchy data for the wave equation in by the measurements of its solution on the boundary of the finite interval. This is…
Relationship between different types of inverse data for the one-dimensional Schrödinger operator on a half-line
A. S. Mikhaylov, V. S. Mikhaylov
We consider inverse dynamical, spectral, quantum and acoustical scattering problems for the Schrödinger operator on the half line. The goal of the paper is to establish the connect…
Dynamic inverse problem for the one-dimensional system with memory
A. E. Choque-Rivero, A. S. Mikhaylov, V. S. Mikhaylov
We study the inverse dynamic problem of recoverying the potential in the one-dimensional dynamical system with memory. The Gelfand--Levitan equations are derived for the kernel of…
Inverse problem for semi-infinite Jacobi matrices and associated Hilbert spaces of analytic functions
Alexander Mikhaylov, Victor Mikhaylov
We consider the dynamic problems for the discrete systems with discrete time associated with finite and semi-infinite Jacobi matrices. The result of the paper is a procedure of ass…
On an application of the Boundary control method to classical moment problems
Alexander Mikhaylov, Victor Mikhaylov
We establish relationships between the classical moments problems which are problems of a construction of a measure supported on a real line, on a half-line or on an interval from…
Inverse problems for finite Jacobi matrices and Krein--Stieltjes strings
Alexander Mikhaylov, Victor Mikhaylov
We consider dynamic inverse problems for a dynamical system associated with a finite Jacobi matrix and for a system describing propagation of waves in a finite Krein-Stieltjes stri…
Inverse Problem for the Schrödinger Equation with Non-self-adjoint Matrix Potential
Sergei Avdonin, Alexander Mikhaylov, Victor Mikhaylov +1
We consider the dynamical system with boundary control for the vector Schrödinger equation on the interval with a non-self-adjoint matrix potential. For this system, we study the i…
Discrete dynamical systems: inverse problems and related topics
Alexander Mikhaylov, Victor Mikhaylov
In this review, we extend the Boundary Control method\, -- \,an approach to inverse problems based on control theory for dynamical systems \, -- \,to inverse problems for discrete…
On an inverse problem in photoacoustic
M. I. Belishev, D. Langemann, A. S. Mikhaylov +1
We consider the problem of reconstruction of the Cauchy data for the wave equation in and by the measurements of its solution on the boundary of the u…
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…
Discretization of the wave equation on a metric graph
Sergei A. Avdonin, Aleksander S. Mikhaylov, Victor S. Mikhaylov +1
The question of what conditions should be set at the nodes of a discrete graph for the wave equation with discrete time is investigated. The variational method for the derivation o…
Dynamic inverse problem for special system associated with Jacobi matrices and classical moment problems
Alexander Mikhaylov, Victor Mikhaylov
We consider the Hamburger, Stieltjes and Hausdorff moment problems, that are problems of the construction of a Borel measure supported on a real line, on a half-line or on an inter…
On the relationship between Weyl functions of Jacobi matrices and response vectors for special dynamical systems with discrete time
A. S. Mikhaylov, V. S. Mikhaylov, S. A. Simonov
We derive special representation for Weyl functions for finite and semi-infinite Jacobi matrices with bounded entries based on a relationship between spectral problem for Jacobi ma…
Inverse dynamic and spectral problems for the one-dimensional Dirac system on a finite tree
A. S. Mikhaylov, V. S. Mikhaylov, G. E. Murzabekova
We consider inverse dynamic and spectral problems for the one dimensional Dirac system on a finite tree. Our aim will be to recover the topology of a tree (lengths and connectivity…
Dynamical inverse problem for Jacobi matrices
A. S. Mikhaylov, V. S. Mikhaylov
We consider the inverse dynamical problem for the dynamical system with discrete time associated with the semi-infinite Jacobi matrix. We solve the inverse problem for such a syste…
Boundary Control method and De Branges spaces. Schrödinger equation, Dirac system and Discrete Schrödinger operator
Alexander S. Mikhaylov, Victor S. Mikhaylov
In the framework of the application of the Boundary Control method to solving the inverse dynamical problems for the one-dimensional Schrödinger and Dirac operators on the half-lin…