Function theory in classical domains : complex potential theory
著者
書誌事項
Function theory in classical domains : complex potential theory
（Encyclopaedia of mathematical sciences / editor-in-chief, R.V. Gamkrelidze, v. 8 . Several complex variables ; 2）
Springer-Verlag, c1994
- : us
- : gw
- : softcover
- タイトル別名
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Several complex variables 2
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注記
Includes bibliographical references and indexes
内容説明・目次
- 巻冊次
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: gw ISBN 9783540181750
内容説明
This volume of the Encyclopaedia contains four parts each ofwhich being an informative survey of a topic in the field ofseveral complex variables. Thefirst deals with residuetheory and its applications to integrals depending onparameters, combinatorial sums and systems of algebraicequations. The second part contains recent results incomplex potential theory and the third part treats functiontheory in the unit ball covering research of the last twentyyears. The latter part includes an up-to-date account ofresearch related to a list of problems, which was publishedby Rudin in 1980. The last part of the book treats complex analysis in thefuturetube. The future tube is an important concept inmathematical physics, especially in axiomatic quantum fieldtheory, and it is related to Penrose'swork on "the complexgeometry of the real world". Researchers and graduate students in complex analysis andmathematical physics will use thisbook as a reference andas a guide to exciting areas of research.
目次
Contents: Multidimensional Residues and Applications by L.A. Ajzenberg, A.K. Tsikh, A.P. Yuzhakov * Plurisubharmonic Functions by A. Sadullaev * Function Theory in the Ball by A.B. Aleksandrov * Complex Analysis in the Future Tube by A.G. Sergeev and V.S. Vladimirov.
- 巻冊次
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: softcover ISBN 9783642633911
内容説明
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 functions in 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.
目次
I. Multidimensional Residues and Applications.- II. Plurisubharmonic Functions.- III. Function Theory in the Ball.- IV. Complex Analysis in the Future Tube.- Author Index.
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