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

Ransford, Thomas

ISBN 10: 0521466547 / ISBN 13: 9780521466547

Published by Cambridge University Press, 1995

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Bibliographic Details

• Title: Potential Theory in the Complex Plane (London Mathematical Society Student Texts, Series Number 28)
• Publisher: Cambridge University Press
• Publication Date: 1995
• Language: English
• ISBN 10: 0521466547
• ISBN 13: 9780521466547
• Binding: Paperback
• Condition: new

About this title

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.

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.