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A short proof of the Cima-Wogen $ L(f)={\rm circle}$ theorem


Authors: José A. Antonino and Salvador Romaguera
Journal: Proc. Amer. Math. Soc. 92 (1984), 391-392
MSC: Primary 30D45; Secondary 30C99, 30D40, 30H05
DOI: https://doi.org/10.1090/S0002-9939-1984-0759659-2
MathSciNet review: 759659
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Abstract: In [1] Cima and Wogen showed that if $ f \in $ ball $ {B_0}$ and $ L(f)$ contains a circle $ \gamma $, then $ \gamma = L(f)$. This note presents a new and straightforward proof of Cima and Wogen's theorem.


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

  • [1] J. A. Cima and W. R. Wogen, Extreme points of the unit ball of the Bloch space $ {B_0}$, Michigan Math. J. 25 (1978), 213-221. MR 0486558 (58:6281)
  • [2] K. J. Wirths, On holomorphic functions satisfying $ \left\vert {f(z)} \right\vert(1 - {\left\vert z \right\vert^2}) \leqslant 1$ in the unit disc, Proc. Amer. Math. Soc. 85 (1982), 19-23. MR 647889 (83c:30030)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1984-0759659-2
Keywords: Holomorphic function, Bloch space, identity principle
Article copyright: © Copyright 1984 American Mathematical Society

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