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Acta Mathematica
Article . 1985 . Peer-reviewed
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Acta Mathematica
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Other literature type . 1985
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Article . 1985
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The Corona theorem for Denjoy domains

Authors: Garnett, John B.; Jones, Peter W.;

The Corona theorem for Denjoy domains

Abstract

The authors prove the famous corona theorem for the space of bounded analytic functions on any Denjoy domain, i.e. a connected open subset \(\Omega\) of the extended complex plane \({\mathcal C}^*\) such that the complement \({\mathcal C}^*\setminus \Omega\) is a subset of the real axis. The proof utilizes the symmetry of the Denjoy domain and the relations between length, harmonic measure, relative to the upper half plane, and analytic capacity of linear sets.

Keywords

Denjoy domain, Banach algebras of differentiable or analytic functions, \(H^p\)-spaces, analytic capacity, Spaces of bounded analytic functions of one complex variable, space of bounded analytic functions, harmonic measure, Ideals, maximal ideals, boundaries, corona theorem

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
30
Average
Top 10%
Top 10%
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gold