Browse by author
Lookup NU author(s): Professor Jim Agler, Professor Nicholas Young
We describe a generalization of the notion of a Hilbert space model of a function in the Schur class of the bidisc. This generalization is well adapted to the investigation of boundary behavior at a mild singularity of the function on the 2-torus. We prove the existence of a generalized model with certain properties corresponding to such a singularity and use this result to solve two function-theoretic problems. The first of these is to characterise the directional derivatives of a function in the Schur class at a singular point on the torus for which the Carath\'eodory condition holds. The second is to obtain a representation theorem for functions in the two-variable Pick class analogous to the refined Nevanlinna representation of functions in the one-variable Pick class.
Author(s): Agler J, Tully-Doyle R, Young NJ
Publication type: Article
Publication status: Published
Journal: Indagationes Mathematicae
Year: 2012
Volume: 23
Issue: 4
Pages: 995-1027
Print publication date: 20/07/2012
Date deposited: 11/07/2012
ISSN (print): 0019-3577
ISSN (electronic): 1872-6100
Publisher: Elsevier BV
URL: http://dx.doi.org/10.1016/j.indag.2012.07.003
DOI: 10.1016/j.indag.2012.07.003
Altmetrics provided by Altmetric