40 citations · 97 across the 15 of their papers we have counts for
19 papers
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\…
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 investiga…
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 \[R_δ\stackrel{\rm def}{=} \{z \in \mathbb{C}: δ<|z|<1\},\]…
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…
On the Operators with Numerical Range in an Ellipse
Jim Agler, Zinaida A. Lykova, N. J. Young
We give new necessary and sufficient conditions for the numerical range of an operator to be a subset of the closed elliptical set $K_δ\subs…
Nonuniqueness of Carathéodory extremal functions on the symmetrized bidisc
Jim Agler, Zinaida Lykova, N. J. Young
We survey the Carathéodory extremal problem on the symmetrized bidisc W…
Intrinsic Directions, Orthogonality and Distinguished Geodesics in the Symmetrized Bidisc
Jim Agler, Zinaida Lykova, N. J. Young
The symmetrized bidisc \[ G \stackrel{\rm{def}}{=}\{(z+w,zw):|z|<1,\ |w|<1\}, \] under the Carathéodory metric, is a complex Finsler space of cohomogeneity in which the geodesi…
Exterior products of operators and superoptimal analytic approximation
Dimitrios Chiotis, Zinaida Lykova, Nicholas Young
We give a new algorithm for the construction of the unique superoptimal analytic approximant of a given continuous matrix-valued function on the unit circle, making use of exterior…
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…
Carathéodory extremal functions on the symmetrized bidisc
Jim Agler, Zinaida Lykova, N. J. Young
We show how realization theory can be used to find the solutions of the Carathéodory extremal problem on the symmetrized bidisc \[ G \stackrel{\rm{def}}{=} \{(z+w,zw):|z|<1, \, |w|…
Realization of functions on the symmetrized bidisc
Jim Agler, N. J. Young
We prove a realization formula and a model formula for analytic functions with modulus bounded by on the symmetrized bidisc \[ G\stackrel{\rm def}{=} \{(z+w,zw): |z|<1, \, |w|…
3-extremal holomorphic maps and the symmetrised bidisc
Jim Agler, Zinaida A. Lykova, N. J. Young
We analyse the 3-extremal holomorphic maps from the unit disc to the symmetrised bidisc , defined to be the set , with a…
Symmetric functions of two noncommuting variables
Jim Agler, N. J. Young
We prove a noncommutative analogue of the fact that every symmetric analytic function of in the bidisc $\D^2$ can be expressed as an analytic function of the variables $z+w…
Extremal holomorphic maps and the symmetrised bidisc
Jim Agler, Zinaida A. Lykova, N. J. Young
We introduce the class of -extremal holomorphic maps, a class that generalises both finite Blaschke products and complex geodesics, and apply the notion to the finite interpolat…
Boundary behavior of analytic functions of two variables via generalized models
J. Agler, R. Tully-Doyle, N. J. Young
We describe a generalization of the notion of a Hilbert space model of a function in the Schur class of the bidisc. This generalization is well adapted to the investigation of boun…
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 $τ\in\tb$ is a point at which $\ph$ has an angular gradient $\nabla\ph(τ)$ then $\nabla\ph(\la) \to \nabla\ph…
Boundary Nevanlinna-Pick interpolation via reduction and augmentation
Jim Agler, N. J. Young
We give an elementary proof of Sarason's solvability criterion for the Nevanlinna-Pick problem with boundary interpolation nodes and boundary target values. We also give a concrete…
The automorphism group of the tetrablock
N. J. Young
The tetrablock is a domain in 3-dimensional complex space that meets 3-dimensional Euclidean space in a regular tetrahedron. It is shown to be inhomogeneous and its automorphism gr…
A Schwarz lemma for a domain related to mu-synthesis
A. A. Abouhajar, M. C. White, N. J. Young
We prove a Schwarz lemma for a domain E in 3-dimensional complex space that arises in connection with a problem in H infinity control theory. We describe a class of automorphisms o…