Realization of functions on the symmetrized bidisc

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.

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

References in corpus (2)

• Holomorphic functions on the symmetrized bidisk - realization, interpolation and extension
• Test Functions, Kernels, Realizations and Interpolation