Potential Theory in the Complex Plane

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September 2003



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.


Preface; A word about notation; 1. Harmonic functions; 2. Subharmonic functions; 3. Potential theory; 4. The Dirichlet problem; 5. Capacity; 6. Applications; Borel measures; Bibliography; Index; Glossary of notation.


'This book is a engaging addition to the estimable London Mathematical Student Text Series. An excellent text; my compliments to the author.' The Mathematical Intelligencer
EAN: 9780521466547
ISBN: 0521466547
Untertitel: 'London Mathematical Society St'. New. Sprache: Englisch.
Erscheinungsdatum: September 2003
Seitenanzahl: 244 Seiten
Format: kartoniert
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