Colloquium Publications 1927; 150 pp; softcover Volume: 6 ISBN10: 0821845993 ISBN13: 9780821845998 List Price: US$39 Member Price: US$31.20 Order Code: COLL/6
 This book studies fundamental properties of the logarithmic potential and their connections to the theory of Fourier series, to potential theory, and to function theory. The material centers around a study of Poisson's integral in two dimensions and of the corresponding Stieltjes integral. The results are then extended to the integrals in terms of Green's functions for general regions. There are some thirty exercises scattered throughout the text. These are designed in part to familiarize the reader with the concepts introduced, and in part to complement the theory. The reader should know something of potential theory, functions of a complex variable, and Lebesgue integrals. The book is based on lectures given by the author in 19241925 at the Rice Institute and at the University of Chicago. Readership Graduate students and research mathematicians interested in differential equations. Table of Contents  Preliminary concepts. Stieltjes integrals and Fourier series
 Functions harmonic within a circle
 Necessary and sufficient conditions. The Dirichlet problems for the circle
 Potentials of a single layer and the Neumann problem
 General simply connected plane regions and the order of their boundary points
 Plane regions of finite connectivity
 Related problems
 Index
