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A Caratheodory theorem for the bidisk via Hilbert space methods
Jim Agler, John E. McCarthy, Nicholas J. Young
If $\ph$ is an analytic function bounded by 1 on the bidisk $\D^2$ and $Ï\in\tb$ is a point at which $\ph$ has an angular gradient $\nabla\ph(Ï)$ then $\nabla\ph(\la) \to \nabla\…
Models of holomorphic functions on the symmetrized skew bidisc
Connor Evans, Zinaida A. Lykova, N. J. Young
The purpose of this paper is to develop the theory of holomorphic functions with modulus bounded by on the symmetrized skew bidisc \[ \mathbb{G}_{r} \stackrel{\rm def}{=} \Big\…
Function theory on the annulus in the dp-norm
Jim Agler, Zinaida Lykova, N. J. Young
In this paper we shall use realization theory to prove new results about a class of holomorphic functions on an annulus \[R_δ\stackrel{\rm def}{=} \{z \in \mathbb{C}: δ<|z|<1\},\…
Boundary behavior of functions in the Schur-Agler class of the polydisc
Jim Agler, Connor Evans, Zinaida Lykova +1
We describe a generalization of the notion of a Hilbert space model of a function in the Schur-Agler class of the polydisc. This generalization is well adapted to the investig…
Function theory in the bfd-norm on an elliptical region
Jim Agler, Zinaida Lykova, Nicholas Young
Let be the open region in the complex plane bounded by an ellipse. The B. and F. Delyon norm on the space of holomorphic functions…
Non-commutative manifolds, the free square root and symmetric functions in two non-commuting variables
Jim Agler, John E. McCarthy, N. J. Young
The richly developed theory of complex manifolds plays important roles in our understanding of holomorphic functions in several complex variables. It is natural to consider manifol…