On canonical solutions of the truncated trigonometric matrix moment problem

Abstract

The main theme of the talk is the discussion of some distinguished solutions of the truncated trigonometric matrix moment problem. Roughly speaking, these solutions are molecular nonnegative Hermitian matrix-valued Borel measures on the unit circle with a special structure. We give some general information on this type of solutions, but we will focus on the so-called nondegenerate situation. In that case, these molecular measures form a family of solutions which can be parametrized by the set of unitary matrices. In particular, we will show that each member of this family offers an extremal property within the solution set of the moment problem in question concerning the weight assigned to some point of the open unit disk. In doing so, an application of the theory of orthogonal matrix polynomials on the unit circle is used to get that insight.status: publishe