Interpolation in Semigroupoid Algebras

2005/07/04 by Dritschel, Michael A., Marcantognini, Stefania, McCullough, Scott · 3 citations
#46E22 (Secondary) #47A13 #47A57 (Primary) #47B38 #47D25 #47L55 #47L75 #FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.math/0507083

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.

Cited by

• Function theoretic aspects of the symmetrized polydisc and generalization
• Function Theory on Tetrablock: Realization, Interpolation, Extension and Toeplitz Corona Theorem
• Function theory of the hexablock and applications to the tetrablock and Euclidean biball

Related

• Test Functions, Kernels, Realizations and Interpolation
• Interpolation in the noncommutative Schur-Agler class
• Realizations via Preorderings with Application to the Schur Class
• Interpolation and transfer-function realization for the noncommutative Schur-Agler class
• Interpolating sequences for the Banach algebras generated by a class of test functions