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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Hermitian forms in function theory

Author: Christine R. Leverenz
Journal: Trans. Amer. Math. Soc. 286 (1984), 675-688
MSC: Primary 30C45
MathSciNet review: 760980
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Abstract: Let $ f$ and $ g$ be analytic in the unit disk $ \vert z\vert\; < 1$. We give a new derivation of the positive semidefinite Hermitian form equivalent to $ \vert g(z)\vert \leq \vert f(z)\vert$, for $ \vert z \vert < 1$, and use it to derive Hermitian forms for various classes of univalent functions. Sharp coefficient bounds for these classes are obtained from the Hermitian forms. We find the specific functions required to make the Hermitian forms equal to zero.

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Article copyright: © Copyright 1984 American Mathematical Society