A note on the Bergman kernel of a certain Hartogs domain
type: Item
instance of: scholarly article
title: A note on the Bergman kernel of a certain Hartogs domain
zbMATH Open document ID: 1267.32002
author: Atsushi Yamamori
published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris
publication date: 2012-11-22T00:00:00Z
review text: Let \(F\) be a non-increasing continuous function from an interval \((0,B]\) into \((0,+\infty].\) Suppose that \(F\) extends to a meromorphic function on \(\{z\in \mathbb{C} : |z|<B\}.\) Let \[ \Omega_{D_F.m}= \Big\{ (z,\zeta ) \in D_F \times \mathbb{C}^m : |\zeta|^2 <\Big(F\big(|z_1|^2\big)- |z_2|^2\Big)^s\Big\}, \] where \(s>0\) and the domain \(D_F\) is defined by \[ D_F= \big\{ z\in \mathbb{C}^2 : |z_1|^2 <B,\; |z_2|^2 < F(|z_1|^2)\big\}. \] The author gives an explicit formula for the Bergman kernel of \(\Omega_{D_F.m},\) where the so-called polylogarithm function \(Li_{-n}(z) = \sum_{k=1}^\infty k^n z^k\) is involved.
Mathematics Subject Classification ID: 32A25
Mathematics Subject Classification ID: 32A05
Mathematics Subject Classification ID: 32A07
zbMATH DE Number: 6109864
zbMATH Keywords: Bergman kernel
zbMATH Keywords: Hartogs domain
reviewed by: Fritz Haslinger
MaRDI profile type: Publication
full work available at URL: j.crma.2012.10.009
OpenAlex ID: W1972197118
cites work: Berezin Quantization and Reproducing Kernels on Complex Domains
cites work: On the Forelli-Rudin construction and weighted Bergman projections
cites work: Weighted Bergman kernels and virtual Bergman kernels
cites work: A remark on the Bergman kernels of the Cartan-Hartogs domains
cites work: The Bergman kernel of the Fock–Bargmann–Hartogs domain and the polylogarithm function
DOI: 10.1016/J.CRMA.2012.10.009
description: scientific article; zbMATH DE number 6109864