Interpolation in Semigroupoid Algebras
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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 Caratheodory-Fejer interpolation problems and their multivariable commutative and noncommutative generalizations, this approach also covers more exotic examples.
33 pages. Updated references and corrected typos. To appear in Journal fur die reine und angewandte Mathematik
33 pages. Updated references and corrected typos. To appear in Journal fur die reine und angewandte Mathematik