An explicit computation of the Bergman kernel function

John P D'Angelo

Research output: Contribution to journalArticlepeer-review

Abstract

We give an explicit computation of the Bergman kernel function on the domain {Mathematical expression} contained in complex Euclidean space of dimension n +m. Here p is any positive number. We obtain the exact formula {Mathematical expression} The constants ck depend on k, n, m, p and we compute them. Writing {Mathematical expression} we obtain the formula {Mathematical expression} and determine d j by evaluating the parameter y at the negative integers. For example {Mathematical expression}

Original languageEnglish (US)
Pages (from-to)23-34
Number of pages12
JournalThe Journal of Geometric Analysis
Volume4
Issue number1
DOIs
StatePublished - Mar 1 1994

Keywords

  • Bergman kernel function
  • Beta function
  • Math Subject Classification: 32H10, 32F15
  • several complex variables
  • weakly pseudoconvex

ASJC Scopus subject areas

  • Geometry and Topology

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