Let B d denote the unit ball of C d , d≥1. Given an inner function I:B d →B 1 , we study the corresponding family σ α [I], α∈∂B 1 , of pluriharmonic Clark measures on the complex sphere. We introduce and investigate related unitary operators U α mapping analogs of model spaces onto L 2 (σ α ), α∈∂B 1 . In particular, we explicitly characterize the set of U α⁎ f such that fσ α is a pluriharmonic measure.
