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arXiv · 1704.00312

Realization of functions on the symmetrized bidisc

Jim Agler·N. J. 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.

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Jim Agler, N. J. Young. 2017-04-02. Realization of functions on the symmetrized bidisc. https://arxiv.org/abs/1704.00312

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