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Interpolation in semigroupoid algebras

Lookup NU author(s): Dr Michael DritschelORCiD, Professor Stefania Marcantognini

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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. © © Walter de Gruyter 2007.

Publication metadata

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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