On canonical solutions of the truncated trigonometric matrix moment problem

Abstract

The truncated trigonometric matrix moment problem is a well studied object. The main theme of the talk is the discussion of some distinguished solutions of that moment problem. Roughly speaking, we discuss certain solutions which 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 case. In that case, the measures in question 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 in the solution set of the moment problem concerning the weight assigned to some point of the open unit disk.Talk in the "Seminario del Cuerpo Academico Ecuaciones de Fisica Matematicas" at the "Universidad Michoacana de San Nicolas de Hidalgo" in Morelia (Mexico)status: publishe