Softcover ISBN:  9780821845998 
Product Code:  COLL/6 
150 pp 
List Price:  $42.00 
MAA Member Price:  $37.80 
AMS Member Price:  $33.60 
Electronic ISBN:  9781470431563 
Product Code:  COLL/6.E 
150 pp 
List Price:  $39.00 
MAA Member Price:  $35.10 
AMS Member Price:  $31.20 

Book DetailsColloquium PublicationsVolume: 6; 1927MSC: Primary 30; 31;
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 1924–1925 at the Rice Institute and at the University of Chicago.
ReadershipGraduate students and research mathematicians interested in differential equations.

Table of Contents

Chapters

Chapter 1. Preliminary concepts. Stieltjes integrals and Fourier series

Chapter 2. Functions harmonic within a circle

Chapter 3. Necessary and sufficient conditions. The Dirichlet problems for the circle

Chapter 4. Potentials of a single layer and the Neumann problem

Chapter 5. General simply connected plane regions and the order of their boundary points

Chapter 6. Plane regions of finite connectivity

Chapter 7. Related problems


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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 1924–1925 at the Rice Institute and at the University of Chicago.
Graduate students and research mathematicians interested in differential equations.

Chapters

Chapter 1. Preliminary concepts. Stieltjes integrals and Fourier series

Chapter 2. Functions harmonic within a circle

Chapter 3. Necessary and sufficient conditions. The Dirichlet problems for the circle

Chapter 4. Potentials of a single layer and the Neumann problem

Chapter 5. General simply connected plane regions and the order of their boundary points

Chapter 6. Plane regions of finite connectivity

Chapter 7. Related problems