Boundary behavior of analytic functions of two variables via generalized models
 Lookup NU author(s)
 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 



Full text is available for this publication: 




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 

Actions   



Altmetrics  



Share   