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The Corona theorem for Denjoy domains. (English) Zbl 0578.30043
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.
Reviewer: A.Zabulionis

30H05 Spaces of bounded analytic functions of one complex variable
46J15 Banach algebras of differentiable or analytic functions, \(H^p\)-spaces
46J20 Ideals, maximal ideals, boundaries
Full Text: DOI
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