Interpolation for multipliers on reproducing kernel Hilbert spaces

Abstract

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 C d \mathbb {C}^d and the reproducing kernels are of the form ( 1 − ⟨ z , w ⟩ − 1 ) I p (1-\langle z,w\rangle ^{-1})I_p and ( 1 − ⟨ z , w ⟩ ) − 1 I q (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.