One-Sided Tangential Interpolation for Hilbert-Schmidt Operator Functions with Symmetries on the Bidisk

Abstract

One-sided tangential interpolation problems for functions with symmetries having values in the set of Hilbert-Schmidt operators and defined on the bidisk are studied. General solutions are described as well as solutions with the minimal scalar and operator-valued norms. Two types of symmetries are considered: (a) componentwise symmetries that operate separately on each component of a general point in the bidisk; (b) interchange symmetry that interchanges the two components of a general point in the bidisk. Applications are made to multipoint tangential interpolation problems of special form.