Remarks on interpolation in reproducing kernel Hilbert spaces

An interpolation problem in reproducing kernel Hilbert spaces is formulated and solved in terms of the minimal solution and the elements of an auxilliary reproducing kernel Hilbert space, subject to a norm constraint. The scheme is illustrated with two particular reproducing kernel Hilbert spaces: the Arveson space and the Bergman space, where the general theorem leads to convenient parametrizations of the solution sets.