CHAPTER 4 - SCHLICHT FUNCTIONS

Abstract

This chapter discusses the schlicht functions. It presents a fundamental theorem on conformal transformation. The chapter proves some elementary properties of schlicht functions. A schlicht function of a schlicht function is schlicht. The chapter focuses on the unit circle. Because by Riemann's theorem, any simply-connected domain can be mapped on to the unit circle, any schlicht function can be associated with a schlicht function in the unit circle; and the properties of the latter can then be translated into properties of the function whenever the function mapping on to the unit circle is known.