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Abstract
A seminal result of Agler characterizes the so-called Schur-Agler class of functions on the polydisk in terms of a unitary colligation transfer function representation. We generalize this to the unit ball of the algebra of multipliers for a family of test functions over a broad class of semigroupoids. There is then an associated interpolation theorem. Besides leading to solutions of the familiar Nevanlinna-Pick and Carathéodory-Fejér interpolation problems and their multivariable commutative and noncommutative generalizations, this approach also covers more exotic problems.
Received: 2005-07-18
Revised: 2006-02-14
Published Online: 2007-08-07
Published in Print: 2007-06-27
© Walter de Gruyter
