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Potential theory is the broad area of mathematical analysis encompassing such topics as harmonic and subharmonic functions.

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.

Publisher:
Cambridge [England] ; New York : Press Syndicate of the University of Cambridge, 1995

ISBN:
9781107362055

1107362059

9781107366961

1107366968

9780511623776

0511623771

0521461200

9780521461207

0521466547

9780521466547

1107362059

9781107366961

1107366968

9780511623776

0511623771

0521461200

9780521461207

0521466547

9780521466547

Characteristics:
1 online resource (x, 232 pages)

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