The Cauchy kernel for cones

Volume 163 / 2004

Sławomir Michalik Studia Mathematica 163 (2004), 21-39 MSC: 32A26, 32D15. DOI: 10.4064/sm163-1-2

Abstract

A new representation of the Cauchy kernel ${\mathcal K}_{{\mit \Gamma }}$ for an arbitrary acute convex cone ${\mit \Gamma }$ in ${\mathbb R}^n$ is found. The domain of holomorphy of ${\mathcal K}_{{\mit \Gamma }}$ is described. An estimation of the growth of ${\mathcal K}_{{\mit \Gamma }}$ near the singularities is given.

Authors

  • Sławomir MichalikFaculty of Mathematics and Natural Sciences
    College of Science
    Cardinal Stefan Wyszyński University
    Dewajtis 5
    01-815 Warszawa, Poland
    e-mail

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