Boundary behavior of the Bergman kernel for generalized Fock-Bargmann-Hartogs domains

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Abstract

In this paper, we study the Bergman kernel for the Hartogs type domain Dμ,p:={(z,ζ)∈C×Cn:‖ζ‖2<e−μ|z|p}. In particular, we compute the explicit form of the Bergman kernel for [Formula presented] for any positive integer m. The relations between the Mittag-Leffler function and the generalized Fock kernel are investigated. Using the explicit formula, we study the asymptotic behavior of the Fock kernel and the boundary behavior of the Bergman kernel on the diagonal for the generalized Fock-Bargmann-Hartogs domains [Formula presented].

Original languageEnglish
Article number125909
JournalJournal of Mathematical Analysis and Applications
Volume509
Issue number1
DOIs
Publication statusPublished - 1 May 2022

Keywords

  • Bergman kernel
  • Boundary behavior
  • Generalized Fock space
  • Generalized Fock-Bargmann-Hartogs domains
  • Mittag-Leffler function

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