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Lookup NU author(s): Dr Michael DritschelORCiD, Professor Stefania Marcantognini
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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 Carathéodory-Fejér interpolation problems and their multivariable commutative and noncommutative generalizations, this approach also covers more exotic problems. © © Walter de Gruyter 2007.
Author(s): Dritschel MA, Marcantognini S, McCullough S
Publication type: Article
Publication status: Published
Journal: Journal fur die Reine und Angewandte Mathematik
Year: 2007
Issue: 606
Pages: 1-40
ISSN (print): 0075-4102
ISSN (electronic): 1435-5345
Publisher: Walter de Gruyter GmbH & Co. KG
URL: http://dx.doi.org/10.1515/CRELLE.2007.033
DOI: 10.1515/CRELLE.2007.033
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