Interpolation for multipliers on reproducing kernel Hilbert spaces

All solutions of a tangential interpolation problem for contractive multipliers between two reproducing kernel Hilbert spaces of analytic vector-valued functions are characterized in terms of certain positive kernels. In a special important case when the spaces consist of analytic functions on the unit ball of $\mathbb{C} ^d$ and the reproducing kernels are of the form $(1-\langle z,w\rangle^{-1})I_p$ and $(1-\langle z,w\rangle)^{-1}I_q$, the characterization leads to a parametrization of the set of all solutions in terms of a linear fractional transformation.