Textbook in PDF format

The material of this book is the outgrowth of a course of lectures which I have given from time to time at Harvard University on the subject of Dirichlet series and Laplace integrals. It is designed for students who have such a knowledge of analysis as might be obtained by reading the more fundamental parts of the familiar text of E.C. Titchmarsh on the theory of functions. I have taken pains to include proofs of results which such a student might not know even though they might be available elsewhere. For example, the first chapter is devoted largely to the study of the Riemann-Stieltjes integral. Although this material is in constant use by analysts it seems not to have been collected in .convenient form. There are only a few instances where I have had to depart from this aim of having the book complete in itself. If he desires, the student may omit such parts without losing the fundamental ideas.
The Stieltjes Integral
The Laplace Transform
The Moment Problem
Absolutely and Completely Monotonic Functions
Tauberian Theorems
The Bilateral Laplace Transform
Inversion and Representation Problems for the Laplace Transform
The Stieltjes Transform