Boundary behavior of analytic functions of two variables via generalized models
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 Professor Jim Agler
 Professor Nicholas Young




Author(s)   Agler J, TullyDoyle R, Young NJ 
Publication type   Article 
Journal   Indagationes Mathematicae 
Year   2012 
Volume   23 
Issue   4 
Pages   9951027 
ISSN (print)   00193577 
ISSN (electronic)   18726100 



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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 2torus. We prove the existence of a generalized model with certain properties corresponding to such a singularity and use this result to solve two functiontheoretic 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 twovariable Pick class analogous to the refined Nevanlinna representation of functions in the onevariable Pick class. 



Publisher   Elsevier BV 
URL   http://dx.doi.org/10.1016/j.indag.2012.07.003 
DOI   10.1016/j.indag.2012.07.003 

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