A short proof of the Cima-Wogen $L(f)=\textrm {circle}$ theorem
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- by JosΓ© A. Antonino and Salvador Romaguera
- Proc. Amer. Math. Soc. 92 (1984), 391-392
- DOI: https://doi.org/10.1090/S0002-9939-1984-0759659-2
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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 Wogenβs theorem.References
- Joseph A. Cima and Warren R. Wogen, Extreme points of the unit ball of the Bloch space ${\cal B}_{0}$, Michigan Math. J. 25 (1978), no.Β 2, 213β222. MR 486558
- Karl-Joachim Wirths, On holomorphic functions satisfying $\,f(z)(1-z^{2})\leq 1$ in the unit disc, Proc. Amer. Math. Soc. 85 (1982), no.Β 1, 19β23. MR 647889, DOI 10.1090/S0002-9939-1982-0647889-8
Bibliographic Information
- © Copyright 1984 American Mathematical Society
- 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