Bernd Fritzsche

Semiseparable Integral Operators and Explicit Solution of an Inverse Problem for a Skew-Self-Adjoint Dirac-Type System

Inverse problem to recover the skew-self-adjoint Dirac-type system from the generalized Weyl matrix function is treated in the paper. Sufficient conditions under which the unique solution of the inverse problem exists, are formulated in terms of the Weyl function and a procedure to solve the inverse problem is given. The case of the generalized Weyl functions of the form

On a moment problem for rational matrix-valued functions

{\phi(\lambda)\,{\rm exp}\{-2i{\lambda}D\}}

Topics in interpolation theory

, where

Skew-Self-Adjoint Dirac System with a Rectangular Matrix Potential: Weyl Theory, Direct and Inverse Problems

{\phi}

Recovery of the Dirac system from the rectangular Weyl matrix function

is a strictly proper rational matrix function and D = D* ≥ 0 is a diagonal matrix, is treated in greater detail. Explicit formulas for the inversion of the corresponding semiseparable integral operators and recovery of the Dirac-type system are obtained for this case.

A Truncated Matricial Moment Problem on a Finite Interval. The Case of an Odd Number of Prescribed Moments

The main goal of this paper is to study the truncated matricial moment problem on a finite closed interval by using the FMI method of V.P. Potapov. The solvability of the problem is characterized by the fact that two block Hankel matrices built from the data of the problem are nonnegative Hermitian. An essential step to solve the problem under consideration is to derive an effective coupling identity between both block Hankel matrices (see Proposition 2.2). In the case that these block Hankel matrices are both positive Hermitian we parametrize the set of solutions via a linear fractional transformation the generating matrix-valued function of which is a matrix polynomial whereas the set of parameters consists of distinguished pairs of meromorphic matrix-valued functions.