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Characterizations of some domains via Carath\'eodory extremals

Autor: Agler, J., Lykova, Z. A., Young, N. J.

In this paper we characterize the unit disc, the bidisc and the symmetrized bidisc \[ G =\{(z+w,zw):|z|<1,\ |w|<1\} \] in terms of the possession of small classes of analytic maps into the unit disc that suffice to solve all Carath\'eodory extremal p

Externí odkaz: http://arxiv.org/abs/1802.09067

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The complex geomety of a domain related to $\mu$-synthesis

Autor: Agler, J., Lykova, Z. A., Young, N. J.

We describe the basic complex geometry and function theory of the {\em pentablock} $\mathcal{P}$, which is the bounded domain in $\mathbb{C}^3$ given by \[ \mathcal{P}= \{(a_{21}, \mathrm{tr} A, \det A): A= \begin{bmatrix} a_{ij}\end{bmatrix}_{i,j=1}

Externí odkaz: http://arxiv.org/abs/1403.1960

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Boundary behavior of analytic functions of two variables via generalized models

Autor: Agler, J., Tully-Doyle, R., Young, N. J.

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 boundary behavior at a mild singularity of the function on the 2-torus. We

Externí odkaz: http://arxiv.org/abs/1203.6589

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The magic functions and automorphisms of a domain

Autor: Agler, J., Young, N. J.

We introduce the notion of magic functions of a general domain in d-dimensional complex space and show that the set of magic functions of a given domain is an intrinsic complex-geometric object. We determine the set of magic functions of the symmetri

Externí odkaz: http://arxiv.org/abs/0709.0096

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