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: 0521461200
ISBN 13: 9780521461207
Binding: Hardcover
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 Phragm�n-Lindel�f principle, the Rad�-Stout theorem, Lindel�f'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.

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