Encyclopaedia of Mathematical Sciences

Several Complex Variables II

Function Theory in Classical Domains Complex Potential Theory

Editors: Khenkin, G.M., Vitushkin, A.G. (Eds.)

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About this book

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 potenĀ­ 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.

Table of contents (4 chapters)

  • Multidimensional Residues and Applications

    Aizenberg, L. A. (et al.)

    Pages 1-58

  • Plurisubharmonic Functions

    Sadullaev, A.

    Pages 59-106

  • Function Theory in the Ball

    Aleksandrov, A. B.

    Pages 107-178

  • Complex Analysis in the Future Tube

    Sergeev, A. G. (et al.)

    Pages 179-253

Buy this book

eBook $99.00
price for USA (gross)
  • ISBN 978-3-642-57882-3
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $129.00
price for USA
  • ISBN 978-3-642-63391-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Several Complex Variables II
Book Subtitle
Function Theory in Classical Domains Complex Potential Theory
Editors
  • G.M. Khenkin
  • A.G. Vitushkin
Translated by
King, J.R., Gauthier, P.M.
Series Title
Encyclopaedia of Mathematical Sciences
Series Volume
8
Copyright
1994
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-642-57882-3
DOI
10.1007/978-3-642-57882-3
Softcover ISBN
978-3-642-63391-1
Series ISSN
0938-0396
Edition Number
1
Number of Pages
VII, 262
Additional Information
Original Russian edition published by VINITI, Moscow, 1985
Topics