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Lookup NU author(s): Dr Michael DritschelORCiD, Daniel Estevez Sanchez
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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
URL: https://doi.org/10.1112/jlms.12003
DOI: 10.1112/jlms.12003
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