15 citations · 44 across the 14 of their papers we have counts for
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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…
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 an…