Abstract

Let Bd denote the unit ball of Cd, d≥1. Given an inner function I:Bd→B1, we study the corresponding family σα[I], α∈∂B1, of pluriharmonic Clark measures on the complex sphere. We introduce and investigate related unitary operators Uα mapping analogs of model spaces onto L2(σα), α∈∂B1. In particular, we explicitly characterize the set of Uα⁎f such that fσα is a pluriharmonic measure.

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