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Interpolation in Semigroupoid Algebras

Michael A. Dritschel·Stefania Marcantognini·Scott McCullough
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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 Caratheodory-Fejer interpolation problems and their multivariable commutative and noncommutative generalizations, this approach also covers more exotic examples.

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Michael A. Dritschel, Stefania Marcantognini, Scott McCullough. 2006-12-20. Interpolation in Semigroupoid Algebras. https://arxiv.org/abs/math/0507083

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