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Results in Mathematics

, Volume 35, Issue 1–2, pp 161–174 | Cite as

A Domain Integral Equation for the Bergman Kernel

  • A. H. M. Murid
  • M. Z. Nashed
  • M. R. M. Razali
Article

Abstract

Certain integral operators involving the Szegö, the Bergman and the Cauchy kernels are known to have the reproducing property. Both the Szegö and the Bergman kernels have series representations in terms of an orthonormal basis. In this paper we derive the Cauchy kernel by means of biorthogonality. The ideas involved are then applied to construct a non-Hermitian kernel admitting a reproducing property for a space associated with the Bergman kernel. The construction leads to a domain integral equation for the Bergman kernel.1 2

En]Keywords

Szegö kernel Bergman kernel biorthogonality integral equation 

Math. Subject Classification

30C40 45B05 

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Copyright information

© Birkhäuser Verlag, Basel 1999

Authors and Affiliations

  • A. H. M. Murid
    • 1
  • M. Z. Nashed
    • 1
  • M. R. M. Razali
    • 2
  1. 1.Department of Mathematics, Faculty of ScienceUniversiti Teknologi MalaysiaJohor BahruMalaysia
  2. 2.Department of Mathematical SciencesUniversity of DelawareNewarkUSA

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