23 papers · 1 filter
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…
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…