Bolotnikov, Realization and interpolation for Schur-Agler-class functions on domains with matrix polynomial defining function in C
- V.J.A. Ball
- J. Funct. Anal
The class of Schur-Agler functions over a domain D ⊂ Cd is defined as the class of holomorphic operator-valued functions on D for which a certain von Neumann inequality is satisfied when a commuting tuple of operators satisfying a certain polynomial norm inequality is plugged in for the variables. Such functions are alternatively characterized as those having a linear-fractional presentation which identifies them as transfer functions of a certain type of conservative structured multidimensional linear system. There now has been introduced a noncommutative version of the Schur-Agler class which consists of formal power series in noncommuting indeterminants satisfying a noncommutative version of the von Neumann inequality when a tuple of operators (not necessarily commuting) coming from a noncommutative operator ball are plugged in for the formal indeterminants. Formal power series in this noncommutative Schur-Agler class in turn are characterized as those having a certain linear-fractional presentation in noncommuting variables identifying them as transfer functions of a recently introduced class of conservative structure multidimensional linear systems having evolution along a free semigroup rather than along an integer lattice. The purpose of this paper is to extend the previously developed interpolation theory for the commutative Schur-Agler class to this noncommutative setting.