For a large class of unitarily invariant reproducing kernel functions K on the unit ball \(\mathbb B_d\) in C^d\), we characterize K-inner as admitting suitable transfer function realization. We associate with each K-contraction T ∈ L(H)d canonical operator-valued and extend uniqueness theorem Arveson for minimal K-dilations to our setting. thus generalize results Olofsson m-hypercontractions d...