Functionals of rational type over the class 𝑆

Abstract

Let L L be a continuous linear functional on the space of functions holomorphic in the unit disk, and let f f be a function in the class S S for which Re L L achieves its maximum on S S . Then L L is said to be of rational type if the expression L ( f 2 / ( f − w ) ) L({f^2}/(f - w)) , which occurs in Schiffer’s differential equation, is a rational function of w w . Various equivalent formulations of "rational type" are found and an application to the process of arc truncation of support points of S S is made.