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Some ℂN capacities and applications

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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

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© 1987 Springer-Verlag

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Korevaar, J. (1987). Some ℂN capacities and applications. In: Berenstein, C.A. (eds) Complex Analysis II. Lecture Notes in Mathematics, vol 1276. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0078960

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  • DOI: https://doi.org/10.1007/BFb0078960

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