Functionals of rational type over the class 𝑆

Brickman, Louis

doi:10.1090/S0002-9939-1984-0759655-5

Functionals of rational type over the class $S$
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Proc. Amer. Math. Soc. 92 (1984), 372-376 Request permission

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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