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Proceedings of the American Mathematical Society

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



Functionals of rational type over the class $ S$

Author: Louis Brickman
Journal: Proc. Amer. Math. Soc. 92 (1984), 372-376
MSC: Primary 30C55; Secondary 30C70
MathSciNet review: 759655
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Abstract: Let $ L$ be a continuous linear functional on the space of functions holomorphic in the unit disk, and let $ f$ be a function in the class $ S$ for which Re $ L$ achieves its maximum on $ S$. Then $ L$ is said to be of rational type if the expression $ L({f^2}/(f - w))$, which occurs in Schiffer's differential equation, is a rational function of $ w$. Various equivalent formulations of "rational type" are found and an application to the process of arc truncation of support points of $ S$ is made.

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Article copyright: © Copyright 1984 American Mathematical Society