  The Schur-Agler class consists of functions over a domain satisfying an
appropriate von Neumann inequality. Originally defined over the polydisk, the
idea has been extended to general domains in multivariable complex Euclidean
space with matrix polynomial defining function as well as to certain
multivariable noncommutative-operator domains with a noncommutative
linear-pencil defining function. Still more recently there has emerged a free
noncommutative function theory (functions of noncommuting matrix variables
respecting direct sums and similaritytransformations). The purpose of the
present paper is to extend the Schur-Agler-class theory to the free
noncommutative functionsetting. This includes the positive-kernel-decomposition
characterization of the class, transfer-function realization and Pick
interpolation theory. A special class of defining functions is identified for
which the associated Schur-Agler class coincides with the
contractive-multiplier class on an associated noncommutative reproducing kernel
Hilbert space; in this case, solution of the Pick interpolation problem is in
terms of the complete positivity of an associated Pick matrix which is
explicitly determined from the interpolation data.
