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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.
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"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
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- Date Published: April 1995
- format: Paperback
- isbn: 9780521466547
- length: 244 pages
- dimensions: 228 x 151 x 13 mm
- weight: 0.345kg
- availability: Available
Table of Contents
A word about notation
1. Harmonic functions
2. Subharmonic functions
3. Potential theory
4. The Dirichlet problem
Glossary of notation.
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