Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Parts in $ H\sp{\infty }$ with homeomorphic analytic maps


Authors: Eric Alan Gerber and Max L. Weiss
Journal: Proc. Amer. Math. Soc. 83 (1981), 315-318
MSC: Primary 46J15; Secondary 30H05
DOI: https://doi.org/10.1090/S0002-9939-1981-0624921-8
MathSciNet review: 624921
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Hoffman characterized the parts of $ {H^\infty }$ as either singleton points or analytic discs. He showed that a part belongs to the latter category if and only if it is hit by the closure of an interpolating sequence and that there are cases where a corresponding analytic map is a homeomorphism and cases where it is not. We show that there is no class, $ \mathcal{C}$, of subsets of the open unit disc such that an analytic map of a part $ P$ is a homeomorphism if and only if $ P$ is hit by the closure of some set in $ \mathcal{C}$.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 46J15, 30H05

Retrieve articles in all journals with MSC: 46J15, 30H05


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1981-0624921-8
Keywords: $ {H^\infty }$, parts, homeomorphic analytic maps
Article copyright: © Copyright 1981 American Mathematical Society

American Mathematical Society