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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Support points and double poles


Author: Say Song Goh
Journal: Proc. Amer. Math. Soc. 122 (1994), 463-468
MSC: Primary 30C50; Secondary 30C70
MathSciNet review: 1197537
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Abstract: This paper gives some sufficient conditions for support points of the class S of univalent functions to be rotations of the Koebe function $ k(z) = z{(1 - z)^{ - 2}}$. If f is a support point associated with a continuous linear functional L and if the function $ \Phi (w) = L({f^2}/(f - w))$ does not have a double pole, then under some mild additional assumptions, a rational support point f must be a rotation of the Koebe function. The situation is more complicated when $ \Phi $ has a double pole. However, we are able to prove the two-functional conjecture for derivative functionals, where $ \Phi $ has a double pole.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1994-1197537-4
PII: S 0002-9939(1994)1197537-4
Keywords: Univalent functions, variational methods, algebraic functions, the two-functional conjecture, derivative functionals
Article copyright: © Copyright 1994 American Mathematical Society