Some ℂN capacities and applications

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


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.


Green Function Homogeneous Polynomial Formal Power Series Plurisubharmonic Function Mixed Derivative 
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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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