Models of Holomorphic Functions on the Symmetrized Skew Bidisc
Abstract
Abstract The purpose of this paper is to develop the theory of holomorphic functions with modulus bounded by 1 on the symmetrized skew bidisc $$ \mathbb {G}_{r} {\mathop {=}\limits ^\textrm{def}} \Big \{( \lambda _{1}+r\lambda _{2} ,r\lambda _{1}\lambda _{2}): \lambda _{1}\in \mathbb {D}, \lambda _{2}\in \mathbb {D}\Big \}, $$ G r = def { ( λ 1 + r λ 2 , r λ 1 λ 2 ) : λ 1 ∈ D , λ 2 ∈ D } , for a fixed $$r \in (0,1)$$ r ∈ ( 0 , 1 ) . We show the existence of a realization formula and a model formula for such holomorphic functions.
Fields of Study & Subjects
Holomorphic and Operator Theory
Geometry and complex manifolds
Algebraic and Geometric Analysis
Publication details
- Journal / source
- Integral Equations and Operator Theory
- Publisher
- Springer Science and Business Media LLC
- Volume
- 98
- Issue
- 2
- Pages
- 18–18
- Publication date
- 18 April 2026
- Language
- EN