Potential Theory in the Complex Plane (London Mathematical Society Student Texts Book 28) 1st Edition by Thomas Ransford (PDF)

Description

Potential theory is the broad area of mathematical analysis encompassing such topics as harmonic and subharmonic functions, the Dirichlet problem, harmonic measure, Green’s functions, potentials and capacity. This is an introduction to the subject suitable for beginning graduate students, concentrating on the important case of two dimensions. This permits a simpler treatment than other books, yet is still sufficient for a wide range of applications to complex analysis; these include Picard’s theorem, the Phragmén–Lindelöf principle, the Koebe one-quarter mapping theorem and a sharp quantitative form of Runge’s theorem. In addition there is a chapter on connections with functional analysis and dynamical systems, which shows how the theory can be applied to other parts of mathematics, and gives a flavour of some recent research. Exercises are provided throughout, enabling the book to be used with advanced courses on complex analysis or potential theory.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐This book is a must-have for those who want to learn potential theory. Ransford has written an extensive book, containing a choice of classical material and exercises which make the reader understand theorems more at depth, just like a good book should. I am a gradstudent in complex analysis and this book has helped me get a good grip of potential theory in one variable.After having (tried to) read several great but difficult classical books on the subject, I was recommended this one, and it has made potential theory accessible and understandable for me. After having read it I was ready for e.g. “Potential theory in modern function theory” by M.Tsuji.In the preface of the book, Ransford expresses a wish that his book bridge the gap between “encyclopaedic treatises on the subject” and “excellent books on complex variables, each containing a useful chapter on potential theory, but which did not go nearly far enough”. In my opinion he has succeeded.

⭐Ce livre est excellent. Je l’ai lu en partant de zéro sur le sujet, et n’ai aucune difficulté à le suivre. L’auteur arrive très bien à faire passer ses idées et concepts, et le tout est bien organisé.

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