The Theory of Functions

Abstract

This is a book on complex analysis, followed by some measure theory. It is the complex analysis part which is superb. Titchmarsh is one of those rare authors that manage to motivate the results, get them with rigour and clarity and, especially, select theorems so well that you always find what you need for applications. It's like the famous short table of integrals in the famous, multi-edition, ''Handbook of Physics and Chemistry''. It was so wisely made that it was said that when you could not find in it the integral you needed, you probably went wrong somewhere. So is the venerable Theory of Functions. It is particularly good in asymptotic theorems like Phragmen-Lindelof's, or in the treatment of analytic continuation.