Potential Theory in the Complex Plane (London Mathematical Society Student Texts, Series Number 28) - Hardcover

Ransford, Thomas

Hardcover

ISBN 10: 0521461200 ISBN 13: 9780521461207

Publisher: Cambridge University Press, 1995

Synopsis

Ransford provides an introduction to the subject, concentrating on the important case of two dimensions, and emphasizing its links with complex analysis. This is reflected in the large number of applications, which include Picard's theorem, the Phragmén-Lindelöf principle, the Radó-Stout theorem, Lindelöf's theory of asymptotic values, the Riemann mapping theorem (including continuity at the boundary), the Koebe one-quarter theorem, Hilbert's lemniscate theorem, and the 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 flavor of some recent research in the area.

About this title

Book Description

Potential theory is the broad area of mathematical analysis encompassing harmonic and subharmonic functions, the Dirichlet problem, harmonic measure, Green's functions, potentials and capacity. This introduction concentrates on the important case of two dimensions, and emphasizes its links with complex analysis.

Review

"Graduate students and researchers in complex analysis will find in this book most of the potential theory that they are likely to need...this attractive book is recommended." Mathematical Reviews

Edition details

• Publisher: Cambridge University Press
• Publication date: 1995
• Language: English
• ISBN 10: 0521461200
• ISBN 13: 9780521461207
• Binding: Hardcover
• Edition number: 1
• Number of pages: 244