Domains of Holomorphy and Pseudoconvexity

  • R. Michael Range
Part of the Graduate Texts in Mathematics book series (GTM, volume 108)


In 1906 F. Hartogs discovered the first example exhibiting the remarkable extension properties of holomorphic functions in more than one variable. It is this phenomenon, more than anything else, which distinguishes function theory in several variables from the classical one-variable theory. Hartogs’ discovery marks the beginning of a genuine several-variable theory, in which fundamental new concepts like domains of holomorphy and the various notions of convexity used to characterize them have become indispensable. In particular, the property now generally referred to as “pseudoconvexity” originates with Hartogs, and even today it still is one of the richest sources of intriguing phenomena and deep questions in complex analysis. (See, for example, the remarks at the end of §2.8.) We will say more about this in Chapter VII.


Pseudoconvex Domain Subharmonic Function Plurisubharmonic Function Holomorphic Extension Analytic Disc 
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Copyright information

© Springer Science+Business Media New York 1986

Authors and Affiliations

  • R. Michael Range
    • 1
  1. 1.Department of Mathematics and StatisticsState University of New York at AlbanyAlbanyUSA

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