Nevanlinna formula for the truncated matrix trigonometric moment problem

Abstract

This paper is a continuation of our investigation on the truncated matrix trigonometric moment problem begun in Ukr. Mat. Zh. - 2011. - 63, № 6. - P. 786-797. In the present paper, we obtain the Nevanlinna formula for this moment problem in the general case. We assume here that there is more than one moment and the moment problem is solvable and has more than one solution. The coefficients of the corresponding matrix linear fractional transformation are expressed in explicit form via prescribed moments. Simple determinacy conditions for the moment problem are presented.