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Strict contractions on a Hilbert space have a functional calculus with functions that are analytic in the unit disc of the complex plane; an estimate of the norm is then provided by von Neumann's inequality. We consider functions that satisfy related inequalities with respect to multioperators connected to certain domains in C n ; a representation formula and a Nevanlinna-Pick type theorem are obtained.doi:10.1090/s0002-9939-02-06321-9 fatcat:hfzpu3snuzb4fg3mxa6amgawq4