28 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 th…
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…
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…
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…