Graduate Texts in Mathematics

3 primary works

Functions of One Complex Variable I

by John B Conway

Published 16 October 1973

"This book presents a basic introduction to complex analysis in both an interesting and a rigorous manner. It contains enough material for a full year's course, and the choice of material treated is reasonably standard and should be satisfactory for most first courses in complex analysis. The approach to each topic appears to be carefully thought out both as to mathematical treatment and pedagogical presentation, and the end result is a very satisfactory book." --MATHSCINET

A Course in Functional Analysis

by John B Conway

Published 13 December 1984

This book is intended as a textbook for a one term course on functional analysis for graduate students. Unlike most modern treatments, this book starts from the particular and works its way up to the more general, thus promoting greater intuition in the reader. Appeal to the intuition of the student is aided by a wide variety of examples and exercises. In this new second edition, the chapter on Fredholm Theory has been completely rewritten and simplified. Additionally, numerous new exercises, comments and bibliographical notes have been included throughout the text.

Functions of One Complex Variable II

by John B Conway

Published 19 May 1995

This book discusses a variety of problems which are usually treated in a second course on the theory of functions of one complex variable, the level being gauged for graduate students. It treats several topics in geometric function theory as well as potential theory in the plane, covering in particular: conformal equivalence for simply connected regions, conformal equivalence for finitely connected regions, analytic covering maps, de Branges' proof of the Bieberbach conjecture, harmonic functions, Hardy spaces on the disk, potential theory in the plane. A knowledge of integration theory and functional analysis is assumed.