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Thin sequences in the corona of \(H ^{\infty }\). (English) Zbl 1278.30056

Summary: We consider several conditions for sequences of points in \(M(H ^{\infty })\) and establish relations between them. We show that every interpolating sequence for \(QA\) of nontrivial points in the corona \(M(H^\infty )\backslash \mathbb{D}\) of \(H ^{\infty }\) is a thin sequence for \(H ^{\infty }\), which satisfies an additional topological condition. The discrete sequences in the Shilov boundary of \(H ^{\infty }\) necessarily satisfy the same condition.

MSC:

30H05 Spaces of bounded analytic functions of one complex variable
30H50 Algebras of analytic functions of one complex variable
46J15 Banach algebras of differentiable or analytic functions, \(H^p\)-spaces
30E10 Approximation in the complex plane
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