Several Complex Variables II by Khenkin, G.M.; Vitushkin, A.G.; Gauthier, P.M.; King, J.R.;

Function Theory in Classical Domains Complex Potential Theory

Series: Encyclopaedia of Mathematical Sciences; 8;

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Product details:

Edition number Softcover reprint of the original 1st ed. 1994
Publisher Springer Berlin Heidelberg
Date of Publication 14 October 2012
Number of Volumes 1 pieces, Book

ISBN 9783642633911
Binding Paperback
No. of pages262 pages
Size 235x155 mm
Weight 421 g
Language English
Illustrations VII, 262 p. Illustrations, black & white

Long description:

Plurisubharmonic functions playa major role in the theory of functions of several complex variables. The extensiveness of plurisubharmonic functions, the simplicity of their definition together with the richness of their properties and. most importantly, their close connection with holomorphic functions have assured plurisubharmonic functions a lasting place in multidimensional complex analysis. (Pluri)subharmonic functions first made their appearance in the works of Hartogs at the beginning of the century. They figure in an essential way, for example, in the proof of the famous theorem of Hartogs (1906) on joint holomorphicity. Defined at first on the complex plane IC, the class of subharmonic functions became thereafter one of the most fundamental tools in the investigation of analytic functions of one or several variables. The theory of subharmonic functions was developed and generalized in various directions: subharmonic functions in Euclidean space IRn, plurisubharmonic functionsin complex space en and others. Subharmonic functions and the foundations ofthe associated classical poten tial theory are sufficiently well exposed in the literature, and so we introduce here only a few fundamental results which we require. More detailed expositions can be found in the monographs of Privalov (1937), Brelot (1961), and Landkof (1966). See also Brelot (1972), where a history of the development of the theory of subharmonic functions is given. This volume of the Encyclopaedia is the second in its subseries on the theory of several complex variables. It contains four parts which deal with topics related to algebraic geometry, potential theory, function theory in the unit ball and twistor geometry. Researchers and graduate students in complex analysis and in mathematical physics will use this book as a reference and as a guide to exciting areas of research.