[28] (with A. C. Schaeffer and D. C. Spencer) The coefficient regions of schlicht functions

Abstract

While colleagues at Stanford in the 1940s, Albert Schaeffer and Donald Spencer produced a series of papers on coefficient regions for schlicht (= univalent) functions, culminating in their well-known book (Schaeffer and Spencer, Coefficient Regions for Schlicht Functions, 1950). Although it appeared earlier, the paper (Schiffer et al., Duke Math. J., 16, 493–527, 1949) is actually a sequel to the book. Largely expository, it provides new insights into the description of coefficient regions as developed in Schaeffer and Spencer (Coefficient Regions for Schlicht Functions, 1950). In particular, it highlights a remarkable connection with Loewner’s theory (Math. Ann., 89, 103–121, 1923) and Schiffer’s paper (C. R. Acad. Sci. Paris, 221, 369–371, 1945).