Realization of functions on the symmetrized bidisc

2017/04/02 by Agler, Jim, Young, N. J. · 2 citations
#30E05 #32A10 #32A26 #47N70 #Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.1704.00312

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|lt;1, |w| lt; 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.

Cited by

• Models of holomorphic functions on the symmetrized skew bidisc
• Hilbert space models and Blaschke frames

Related

• Models of holomorphic functions on the symmetrized skew bidisc
• Carathéodory extremal functions on the symmetrized bidisc
• Determining sets for holomorphic functions on the symmetrized bidisk
• Interpolating sequences and the Toeplitz corona theorem on the symmetrized bidisk
• Holomorphic functions on the symmetrized bidisk II -- Interpolating sequences and the Toeplitz corona theorem