Complex Function Theory is a concise and rigorous introduction to the theory of functions of a complex variable. Written in a classical style, it is in the spirit of the books by Ahlfors and by Saks and Zygmund. Being designed for a one-semester course, it is much shorter than many of the standard texts. Sarason covers the basic material through Cauchy's theorem and applications, plus the Riemann mapping theorem. It is suitable for either an introductory graduate course or an undergraduate course for students with adequate preparation. The first edition was published with the title Notes on Complex Function Theory.To prove the sharpened form of Rungea#39;s theorem, it will suffice to show that any rational function whose poles lie in C\K can be uniformly approximated on K by rational functions whose poles lie in S. Because any rational function can beanbsp;...
|Title||:||Complex Function Theory|
|Publisher||:||American Mathematical Soc. - 2007-12-20|