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Open Mathematics

formerly Central European Journal of Mathematics

Editor-in-Chief: Gianazza, Ugo / Vespri, Vincenzo


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Volume 11, Issue 10

Issues

Volume 13 (2015)

Thin sequences in the corona of H ∞

Dimcho Stankov
  • Faculty of Mathematics and Informatics, Shumen University Konstantin Preslavsky, 115 Universitetska Str., 9712, Shumen, Bulgaria
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/ Tzonio Tzonev
  • Faculty of Mathematics and Informatics, Shumen University Konstantin Preslavsky, 115 Universitetska Str., 9712, Shumen, Bulgaria
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Published Online: 2013-07-20 | DOI: https://doi.org/10.2478/s11533-013-0281-1

Abstract

In this paper we consider several conditions for sequences of points in M(H ∞) 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 ∞ is a thin sequence for H ∞, which satisfies an additional topological condition. The discrete sequences in the Shilov boundary of H ∞ necessarily satisfy the same condition.

MSC: 30H05; 30H50; 46J15

Keywords: Bounded analytic functions; Interpolating sequences; Thin sequences; Corona

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About the article

Published Online: 2013-07-20

Published in Print: 2013-10-01


Citation Information: Open Mathematics, Volume 11, Issue 10, Pages 1843–1849, ISSN (Online) 2391-5455, DOI: https://doi.org/10.2478/s11533-013-0281-1.

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© 2013 Versita Warsaw. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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