English

Realization of functions on the symmetrized bidisc

Complex Variables 2017-04-04 v1

Abstract

We prove a realization formula and a model formula for analytic functions with modulus bounded by 11 on the symmetrized bidisc G=def{(z+w,zw):z<1,w<1}. 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.

Keywords

Cite

@article{arxiv.1704.00312,
  title  = {Realization of functions on the symmetrized bidisc},
  author = {Jim Agler and N. J. Young},
  journal= {arXiv preprint arXiv:1704.00312},
  year   = {2017}
}

Comments

14 pages. To appear in J. Math. Anal. Applications