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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
DOI: https://doi.org/10.1090/S0002-9939-1984-0759655-5
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.


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

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1984-0759655-5
Article copyright: © Copyright 1984 American Mathematical Society

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