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Some ℂN capacities and applications

  • J. Korevaar
Special Year Papers
Part of the Lecture Notes in Mathematics book series (LNM, volume 1276)

Abstract

Homogeneous Siciak-type capacities will be derived from extended Green functions with pole at infinity and from polynomial approximation numbers. The latter describe how well monomials can be approximated on a bounded set E in ℂN by linear combinations of other monomials of the same degree. Such polynomial approximation numbers lead to a precise form of a lemma by Wiegerinck and the author on the estimation of mixed derivatives in terms of directional derivatives of the same order. A number of other applications will be surveyed, including the Sibony-Wong theorem on the growth of entire functions, a result on real-analyticity and a simple edge-of-the-wedge theorem, Siciak’s convergence theorem for polynomial series and Wiegerinck’s results on the Radon transformation and N-dimensional holomorphic extension.

Keywords

Green Function Homogeneous Polynomial Formal Power Series Plurisubharmonic Function Mixed Derivative 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 1987

Authors and Affiliations

  • J. Korevaar
    • 1
  1. 1.Math. InstituteUniv. of AmsterdamAmsterdam

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