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Let L be a continuous linear functional on the space of functions holomorphic in the unit disk, and let / be a function in the class S for which ReL achieves its maximum on S. Then L is said to be of rational type if the expression L(f2/(/ — 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. 1. Introduction. Let H(A) be the topological linear space of holomorphic functions on the unit disk A = {z G C: \z\ < 1}. The class S is the subset of H(A) consisting of univalent functions h with the normalization h(0) = 0, h'(0) = 1. We suppose L is a complex-valued continuous linear functional on H (A), that is L G H(A)*, and that L is nonconstant on 5. Then any function / G S for which Re L(f) = maxRe{L(/i) : h G S} must map A onto the complement of an analytic arc Vf satisfying (except possibly at the finite endpoint)

Functionals of rational type over the class 𝑆