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Nevanlinna showed that Cauchy transforms of probability measures parametrizeall functions from the upper half plane into itself satisfying a certainasymptotic condition at infinity. We show that the correspondence fails ingeneral for the unbounded case for somewhat trivial reasons; however, we showthat in a setting of "homomorphic" operator valued free probability that Cauchytransforms of homomorphic conditional expectations parametrize free Pickfunctions.

Cauchy transforms arising from homomorphic conditional expectations  parametrize free Pick functions but those arising from conditional  expectations do not