On a bitangential interpolation problem for contractive-valued functions on the unit ball Original Research Article

We solve the bitangential interpolation problem with a finite number of interpolation nodes for a multivariable analogue of the Schur class consisting of matrix-valued analytic functions on the ball. The interpolation conditions are formulated via a generalized functional calculus with operator argument, thereby generalizing in a compact way the simple, first-order interpolation conditions considered for this class of functions in earlier work. The description of all solutions is given via a Redheffer transform whose entries are given explicitly in terms of the interpolation data.