Interpolation in Semigroupoid Algebras

Details Interpolation in Semigroupoid Algebras Interpolation in Semigroupoid Algebras

2005-07-04

arxiv.org/abs/math/0507083v3

Mathematics

Functional Analysis

33 pages. Updated references and corrected typos. To appear in Journal fur die reine und angewandte Mathematik

Scientific paper

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.

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