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Realization of functions on the symmetrized bidisc

Lookup NU author(s): Professor Jim Agler, Emeritus Professor Nicholas Young

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Abstract

We prove a realization formula and a model formula for analytic functions with modulus bounded by $1$ on the symmetrized bidisc\[G\stackrel{\rm def}{=} \{(z+w,zw): |z|<1, \, |w| < 1\}.\]As an application we prove a Pick-type theorem giving a criterion for the existence of such a function satisfying a finite set of interpolation conditions.

Publication metadata

Author(s): Agler J, Young NJ

Publication type: Article

Publication status: Published

Journal: Journal of Mathematical Analysis and Applications

Year: 2017

Volume: 453

Issue: 1

Pages: 227-240

Print publication date: 01/09/2017

Online publication date: 05/04/2017

Acceptance date: 01/04/2017

Date deposited: 08/04/2017

ISSN (print): 0022-247X

ISSN (electronic): 1096-0813

Publisher: Elsevier

URL: https://doi.org/10.1016/j.jmaa.2017.04.003

DOI: 10.1016/j.jmaa.2017.04.003

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