A family of schlicht functions are the rotated Koebe functions
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In 1948 Schaeffer shared the B�cher memorial prize with Donald Spencer for their joint work on schlicht functions.
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His Ph . D . thesis, on complex analysis, was titled " Some results in the theory of Schlicht functions ".
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This conjecture introduced the key idea of bounding various quadratic functions of the coefficients rather than the coefficients themselves, which is equivalent to bounding norms of elements in certain Hilbert spaces of schlicht functions.
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Duren's research and expository writing deals with function theory and functional analysis, including Hardy spaces, schlicht functions, harmonic analysis, geometric function theory, potential theory, and special functions.
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Schaeffer worked with Donald Spencer at Stanford University on variational problems of conformal mapping, " e . g . " coefficient ranges for schlicht functions ( functions analytic and one-to-one ).
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In 1955, he became especially interested in complex function theory and made a significant contribution to mathematics in his study of a special class of Schlicht functions, for which he showed that the Bieberbach Conjecture held.
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