# ePrints

## Traces of analytic uniform algebras on subvarieties and test collections

Lookup NU author(s): Dr Michael DritschelORCiD, Daniel Estevez Sanchez

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### Abstract

Given a complex domain $\Omega$ and analytic functions $\varphi_1,\ldots,\varphi_n : \Omega \to \D$, we give geometric conditions for $H^\infty(\Omega)$ to be generated by functions of the form $g \circ \varphi_k$, $g \in H^\infty(\D)$. We apply these results to the extension of bounded functions on an analytic one-dimensional complex subvariety of the polydisk $\D^n$ to functions in the Schur-Agler algebra of $\D^n$, with an estimate on the norm of the extension. Our proofs use some extension of the techniques of separation of singularities by Havin, Nersessian and Ortega-Cerd\'a.

Author(s): Dritschel MA, Estévez D, Yakubovich D

Publication type: Article

Publication status: Published

Journal: Journal of the London Mathematical Society

Year: 2017

Volume: 95

Issue: 2

Pages: 414-440

Print publication date: 01/04/2017

Online publication date: 15/01/2017

Acceptance date: 13/06/2016

ISSN (print): 0024-6107

ISSN (electronic): 1469-7750

Publisher: Wiley-Blackwell

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