On the truncated matrix power moment problem with an open gap

Abstract: In this paper we study the truncated power moment problem with an odd number of prescribed moments. A Nevanlinna-type formula is derived for this moment problem in the case when the moment problem has more than one solution (the indeterminate case). The coefficients of the corresponding linear fractional transformation are expressed explicitly in terms of the given moments. In the determinate case the solution to the moment problem is constructed, as well. Those solutions of the moment problem, which satisfy the following condition: $M(\Delta)=0$, where $\Delta$ is a prescribed open subset of $\mathbb{R}$, and $M$ is the matrix measure generated by a solution of the moment problem, are described.