47 citations · 297 across the 36 of their papers we have counts for
36 papers
Dynamic representation of the Weyl solution for the Schrödinger operator on the semi-axis
A. S. Mikhaylov, V. S. Mikhaylov
We derive a representation formula for the Weyl solution to the Schrödinger operator on the semi-axis for certain classes of potentials. Our approach is based on relations with the…
On the Weyl function for complex Jacobi matrices
A. S. Mikhaylov, V. S. Mikhaylov
We derive a new representation for the Weyl function associated with the complex Jacobi matrix in the finite and semi-infinite cases. In our approach we exploit connections to the…
On the complex moment problem as a dynamic inverse problem for a discrete system
A. S. Mikhaylov, V. S. Mikhaylov
We consider the complex moment problem, that is the problem of constructing a positive Borel measure on from a given set of moments. We relate this problem to the dyna…
The boundary control approach to the Titchmarsh-Weyl function
S. A. Avdonin, V. S. Mikhaylov, A. V. Rybkin
We link the Boundary Control Theory and the Titchmarsh-Weyl Theory. This provides a natural interpretation of the amplitude due to Simon and yields a new efficient method to ev…
The boundary control approach to inverse spectral theory
S. A. Avdonin, V. S. Mikhaylov
We establish connections between different approaches to inverse spectral problems: the classical Gelfand--Levitan theory, the Krein method, the Simon theory, the approach proposed…
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 inverse problem of the two-velocity tree-like graph
S. A. Avdonin, A. Choque Rivero, G. Leugering +1
In this article the authors continue the discussion in \cite{ALM} about inverse problems for second order elliptic and hyperbolic equations on metric trees from boundary measuremen…
On an inverse problem for tree-like networks of elastic strings
S. A. Avdonin, G. Leugering, V. S. Mikhaylov
We consider the in-plane motion of elastic strings on tree-like network, observed from the 'leaves'. We investigate the inverse problem of recovering not only the physical properti…
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…
Controllability of partial differential equations on graphs
S. A. Avdonin, V. S. Mikhaylov
We study the boundary control problems for the wave, heat, and Schrödinger equations on a finite graph. We suppose that the graph is a tree (i.e., it does not contain cycles), and…
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…
Spectral Estimation Problem in Infinite Dimensional Spaces
S. A. Avdonin, V. S. Mikhaylov
We consider the generalized spectral estimation problem in infinite dimensional spaces. We solve this problem using the boundary control approach to inverse theory and provide an a…
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…
Unified approach to classical equations of inverse problem theory
M. I. Belishev, V. S. Mikhaylov
The boundary control (BC-) method is an approach to inverse problems based upon their deep relations to control and system theory. We show that the classical integral equations 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…
Construction of solutions of Toda lattices by the classical moment problem
Alexander Mikhaylov, Victor Mikhaylov
Making use of formulas of J. Moser for a finite-dimensional Toda lattices, we derive the evolution law for moments of the spectral measure of the semi-infinite Jacobi operator asso…
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…
On inverse dynamical and spectral problems for the wave and Schrödinger equations on finite trees. The leaf peeling method
S. A. Avdonin, V. S. Mikhaylov, K. B. Nurtazina
Interest in inverse dynamical, spectral and scattering problems for differential equations on graphs is motivated by possible applications to nano-electronics and quantum waveguide…
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…